@CodeMercenary Glad it worked!
I just noticed that in the couple weeks since this happened, a new set of Pool Patches was available, so I ran through the usual process to update those and had no issues at all. This time, everything went smoothly, just as it has for the entire time I've had this lab up and running.
So, chalk this up to one of those weird glitches you're bound to see when you use any technology long enough.
As far as I'm concerned, the issue has been resolved. Please feel free to close out the issue.