Sorry. I missed part of your question.
If you return the pipeline output and not the host output, you can return it as JSON which will then be translated to PSCustomObjects by PS if you use Invoke-RestMethod.
Invoke-UAScript -ID $script.ID -FileName "$SessionId.csv" -Integrated | Tee-Object -Variable | Wait-PSUJob -Integrated
$Pipeline = Get-PSUJobPipelineOutput -Job $Job -Integrated
$HostOutput = Get-PSUJobOutput -Job $Job -Integrated
$Pipeline | ConvertTo-Json
It won’t necessarily look exactly the same in the command line since it won’t include type data and the custom formatting may not kick in but give it a shot and see how it goes.