I was able to resolve the issues I was having.
To add a new printer port it needed to be done independently of the name to use. Whereas I was using
Add-PrinterPort -Name $($Printer.PortName.Replace("\\printman\","\\cacitspdquepr1\"))
What I needed to use was
$NewPort = $Printer.PortName.Replace("\\printman\","\\cacitspdquepr1\")
Add-PrinterPort -Name $NewPort
Similarily with Set-Printer, where I was using
Set-Printer -Name $Printer.Name -PortName $($Printer.PortName.Replace("\\OLD\","\\NEW\"))
It needed to be
$ThisPrinter = Get-Printer -Name $Printer.Name
Set-Printer -Name $ThisPrinter.Name -PortName $Printer.PortName.Replace("\\OLD\","\\NEW\")