I found that Power Shell needed enhanced permissions to make changes to DNS (and associated folders and files). After some research I ended up using this code:
pipeline.Commands.AddScript("$pw= convertto-securestring 'adminPassword' -asplaintext –force");
pipeline.Commands.AddScript("$user = New-Object Management.Automation.PSCredential('machine\\Administrator', $pw)");
pipeline.Commands.AddScript("Invoke-Command -ComputerName . -Credential $user -ScriptBlock {"+scriptText+"}");
I recognize that hard coding my admin password is bad form, but time was running out and I was unable to find a better solution.
If anyone else has a better solution, I am open to it.