Replace multiline text in a file using Powershell without using Regex

I have the following Powershell script:

$oldCode =  @"
            <div id="time_estimate">
                <!-- some large table -->
            </div>
"@

$newCode = @"
            <div id="time_estimate">
                                <!-- nested divs and spans -->
                                <div id="contact-form">

                                        <?php include "contact-form.php"; ?>
                                </div>
                        </div>
"@

ls *.html | foreach { 
        $fileContent = [System.Io.File]::ReadAllText($_.FullName)
        $newFileContent = $fileContent.Replace($oldCode, $newCode)
        [System.Io.File]::WriteAllText($_.FullName, $newFileContent)
        Write-Host  "`r`n"
        Write-Host  "Processed - $($_.Name)...`r`n" }

This doesn't seem to be replacing the text. Is it an issue with the multiline strings, or the limits of the Replace() method? I would prefer to do the replace without bringing in regex.