Okay, I was able to get the "Invoke-SwisVerb : Verb Orion.AlertStatus.Acknowledge cannot unpackage parameter 0" error to go away by modifying the array to be:
$res = Invoke-SwisVerb $swis "Orion.AlertStatus" "Acknowledge" @(,$alertKey,$nodeAlias,$alertGroup)
I'm not sure why that got rid of the error, but I saw it done in one of the examples I was looking at earlier so I figured I would try it.
The current issue is that the alert just simply doesn't get acknowledged after running the script. Any idea what I am doing wrong?