Invoke-Command and exe throwing terminating error

I have a wrapper script to execute other scripts remotely (by copying them to the remote computer and running them via Invoke-Command), but I'm having an issue where it behaves differently when run locally than using Invoke-Command.

If I execute this script locally, reg.exe doesn't throw a terminating error, no matter what $ErrorActionPreference is set to.

remote.ps1

$err = 0
# This makes no difference on reg.exe when executing locally, but it does when using Invoke-Command
#$ErrorActionPreference = 'Stop'
try { 
    & reg load HKU\AlreadyLoaded C:\Users\user\ntuser.dat
    "reg.exe exited with code $LastExitCode"
    if ($LastExitCode) { throw 'could not load user hive' }
} catch {
    "Error caught: $_"
    $err = 1
}
"Remote Script exiting with code $err"
exit $err

Output:

ERROR: The process cannot access the file because it is being used by another process.
reg.exe exited with code 1
Error caught: could not load user hive
Remote Script exiting with code 1

wrapper.ps1

$err = 0
$ErrorActionPreference = 'Stop'

try { 
    Invoke-Command -ComputerName foo -ScriptBlock {
        Set-ExecutionPolicy Bypass -Scope Process -Force
        & C:\remote.ps1 
        if ($LastExitCode -gt 0) { throw "Remote script exited with non-zero code" }
    }
} catch {
    Write-Warning $_
    $err = 1
}

"Local Script exiting with code $err"
exit $err
 

Output without $ErrorActionPreference = 'Stop' in remote script: (the exception thrown by reg.exe is caught by wrapper script)

WARNING: ERROR: The process cannot access the file because it is being used by another process.
Local Script exiting with code 1

Output with $ErrorActionPreference = 'Stop' in remote script: (the exception thrown by reg.exe is caught by remote script)

Error caught: ERROR: The process cannot access the file because it is being used by another process.
Remote Script exiting with code 1
WARNING: Remote script exited with non-zero code
Local Script exiting with code 1

I thought of using Invoke-Command with ErrorAction = 'Continue' but then how do I catch errors from the command itself, such as the remote computer being down?

What's the best approach to run a script remotely and have it behave like it was run locally?