Start-Process would be my last resort choice for invoking PowerShell from PowerShell - especially because all I/O becomes strings and not (deserialized) objects.

Two alternatives:

1. If the user is a local admin and PSRemoting is configured

If a remote session against the local machine (unfortunately restricted to local admins) is a option, I'd definitely go with Invoke-Command:

$strings = Invoke-Command -FilePath C:\...\script1.ps1 -ComputerName localhost -Credential $credential

$strings will contain the results.

2. If the user is not an admin on the target system

You can write your own "local-only Invoke-Command" by spinning up an out-of-process runspace by:

1. Creating a PowerShellProcessInstance, under a different login
2. Creating a runspace in said process
3. Execute your code in said out-of-process runspace

I put together such a function below, see inline comments for a walk-through:

function Invoke-RunAs
{
    [CmdletBinding()]
    param(
        [Alias('PSPath')]
        [ValidateScript({Test-Path $_ -PathType Leaf})]
        [Parameter(Position = 0, Mandatory = $true, ValueFromPipeline = $true, ValueFromPipelineByPropertyName = $true)]
        [string]
        ${FilePath},

        [Parameter(Mandatory = $true)]
        [pscredential]
        [System.Management.Automation.CredentialAttribute()]
        ${Credential},

        [Alias('Args')]
        [Parameter(ValueFromRemainingArguments = $true)]
        [System.Object[]]
        ${ArgumentList},

        [Parameter(Position = 1)]
        [System.Collections.IDictionary]
        $NamedArguments
    )

    begin
    {
        # First we set up a separate managed powershell process
        Write-Verbose "Creating PowerShellProcessInstance and runspace"
        $ProcessInstance = [System.Management.Automation.Runspaces.PowerShellProcessInstance]::new($PSVersionTable.PSVersion, $Credential, $null, $false)

        # And then we create a new runspace in said process
        $Runspace = [runspacefactory]::CreateOutOfProcessRunspace($null, $ProcessInstance)
        $Runspace.Open()
        Write-Verbose "Runspace state is $($Runspace.RunspaceStateInfo)"
    }

    process
    {
        foreach($path in $FilePath){
            Write-Verbose "In process block, Path:'$path'"
            try{
                # Add script file to the code we'll be running
                $powershell = [powershell]::Create([initialsessionstate]::CreateDefault2()).AddCommand((Resolve-Path $path).ProviderPath, $true)

                # Add named param args, if any
                if($PSBoundParameters.ContainsKey('NamedArguments')){
                    Write-Verbose "Adding named arguments to script"
                    $powershell = $powershell.AddParameters($NamedArguments)
                }

                # Add argument list values if present
                if($PSBoundParameters.ContainsKey('ArgumentList')){
                    Write-Verbose "Adding unnamed arguments to script"
                    foreach($arg in $ArgumentList){
                        $powershell = $powershell.AddArgument($arg)
                    }
                }

                # Attach to out-of-process runspace
                $powershell.Runspace = $Runspace

                # Invoke, let output bubble up to caller
                $powershell.Invoke()

                if($powershell.HadErrors){
                    foreach($e in $powershell.Streams.Error){
                        Write-Error $e
                    }
                }
            }
            finally{
                # clean up
                if($powershell -is [IDisposable]){
                    $powershell.Dispose()
                }
            }
        }
    }

    end
    {
        foreach($target in $ProcessInstance,$Runspace){
            # clean up
            if($target -is [IDisposable]){
                $target.Dispose()
            }
        }
    }
}

Then use like so:

$output = Invoke-RunAs -FilePath C:\path\to\script1.ps1 -Credential $targetUser -NamedArguments @{ClientDevice = "ClientName"}

Note:

• The following solution works with any external program, and captures output invariably as text.

• To invoke another PowerShell instance and capture its output as rich objects (with limitations), see the variant solution in the bottom section or consider Mathias R. Jessen's helpful answer, which uses the PowerShell SDK.

Here's a proof-of-concept based on direct use of the System.Diagnostics.Process and System.Diagnostics.ProcessStartInfo .NET types to capture process output in memory (as stated in your question, Start-Process is not an option, because it only supports capturing output in files, as shown in this answer):

Note:

• Due to running as a different user, this is supported on Windows only (as of .NET Core 3.1), but in both PowerShell editions there.

• Due to needing to run as a different user and needing to capture output, .WindowStyle cannot be used to run the command hidden (because using .WindowStyle requires .UseShellExecute to be $true, which is incompatible with these requirements); however, since all output is being captured, setting .CreateNoNewWindow to $true effectively results in hidden execution.

• Only stdout output is captured below. If you want to capture stderr output too, you'll need to capture it via events, because use of $ps.StandardError.ReadToEnd() alongside $ps.StandardOutput.ReadToEnd() could lead to deadlocks.

# Get the target user's name and password.
$cred = Get-Credential

# Create a ProcessStartInfo instance
# with the relevant properties.
$psi = [System.Diagnostics.ProcessStartInfo] @{
  # For demo purposes, use a simple `cmd.exe` command that echoes the username. 
  # See the bottom section for a call to `powershell.exe`.
  FileName = 'cmd.exe'
  Arguments = '/c echo %USERNAME%'
  # Set this to a directory that the target user
  # is permitted to access.
  WorkingDirectory = 'C:\'                                                                   #'
  # Ask that output be captured in the
  # .StandardOutput / .StandardError properties of
  # the Process object created later.
  UseShellExecute = $false # must be $false
  RedirectStandardOutput = $true
  RedirectStandardError = $true
  # Uncomment this line if you want the process to run effectively hidden.
  #   CreateNoNewWindow = $true
  # Specify the user identity.
  # Note: If you specify a UPN in .UserName
  # (user@doamin.com), set .Domain to $null
  Domain = $env:USERDOMAIN
  UserName = $cred.UserName
  Password = $cred.Password
}

# Create (launch) the process...
$ps = [System.Diagnostics.Process]::Start($psi)

# Read the captured standard output.
# By reading to the *end*, this implicitly waits for (near) termination
# of the process.
# Do NOT use $ps.WaitForExit() first, as that can result in a deadlock.
$stdout = $ps.StandardOutput.ReadToEnd()

# Uncomment the following lines to report the process' exit code.
#   $ps.WaitForExit()
#   "Process exit code: $($ps.ExitCode)"

"Running ``cmd /c echo %USERNAME%`` as user $($cred.UserName) yielded:"
$stdout

The above yields something like the following, showing that the process successfully ran with the given user identity:

Running `cmd /c echo %USERNAME%` as user jdoe yielded:
jdoe

Since you're calling another PowerShell instance, you may want to take advantage of the PowerShell CLI's ability to represent output in CLIXML format, which allows deserializing the output into rich objects, albeit with limited type fidelity, as explained in this related answer.

# Get the target user's name and password.
$cred = Get-Credential

# Create a ProcessStartInfo instance
# with the relevant properties.
$psi = [System.Diagnostics.ProcessStartInfo] @{
  # Invoke the PowerShell CLI with a simple sample command
  # that calls `Get-Date` to output the current date as a [datetime] instance.
  FileName = 'powershell.exe'
  # `-of xml` asks that the output be returned as CLIXML,
  # a serialization format that allows deserialization into
  # rich objects.
  Arguments = '-of xml -noprofile -c Get-Date'
  # Set this to a directory that the target user
  # is permitted to access.
  WorkingDirectory = 'C:\'                                                                   #'
  # Ask that output be captured in the
  # .StandardOutput / .StandardError properties of
  # the Process object created later.
  UseShellExecute = $false # must be $false
  RedirectStandardOutput = $true
  RedirectStandardError = $true
  # Uncomment this line if you want the process to run effectively hidden.
  #   CreateNoNewWindow = $true
  # Specify the user identity.
  # Note: If you specify a UPN in .UserName
  # (user@doamin.com), set .Domain to $null
  Domain = $env:USERDOMAIN
  UserName = $cred.UserName
  Password = $cred.Password
}

# Create (launch) the process...
$ps = [System.Diagnostics.Process]::Start($psi)

# Read the captured standard output, in CLIXML format,
# stripping the `#` comment line at the top (`#< CLIXML`)
# which the deserializer doesn't know how to handle.
$stdoutCliXml = $ps.StandardOutput.ReadToEnd() -replace '^#.*\r?\n'

# Uncomment the following lines to report the process' exit code.
#   $ps.WaitForExit()
#   "Process exit code: $($ps.ExitCode)"

# Use PowerShell's deserialization API to 
# "rehydrate" the objects.
$stdoutObjects = [Management.Automation.PSSerializer]::Deserialize($stdoutCliXml)

"Running ``Get-Date`` as user $($cred.UserName) yielded:"
$stdoutObjects
"`nas data type:"
$stdoutObjects.GetType().FullName

The above outputs something like the following, showing that the [datetime] instance (System.DateTime) output by Get-Date was deserialized as such:

Running `Get-Date` as user jdoe yielded:

Friday, March 27, 2020 6:26:49 PM

as data type:
System.DateTime

rcv.ps1

param(
    $username,
    $password
)

"The user is:  $username"
"My super secret password is:  $password"

execution from another script:

.\rcv.ps1 'user' 'supersecretpassword'

output:

The user is:  user
My super secret password is:  supersecretpassword

What you can do it the following to pass a parameter to a ps1 script.

The first script can be a origin.ps1 where we write:

& C:\scripts\dest.ps1 Pa$$w0rd parameter_a parameter_n

Th destination script dest.ps1 can have the following code to capture the variables

$var0 = $args[0]
$var1 = $args[1]
$var2 = $args[2]
Write-Host "my args",$var0,",",$var1,",",$var2

And the result will be

my args Pa$$w0rd, parameter_a, parameter_n