As a postscript, hopefully, to this issue I will say that @AlnoorCassim was incredibly helpful, although some assembly was required. At least you got me thinking in the right direction, sir.
If anyone else gets this issue I will include what I hope is the resolution, although as the client has gone dark on me I won't know if the resolution is totally effective until we actually do the migration. Warning, verbose dissertation ahead!
Here's what I did:
If you remember where we left off Mr. Cassim suggested I remove the SY_System file that might be in the MAS_System folder, where it shouldn't be, so the system would use the one in the MAS_SYSTEM database, where it should be looking for it.
This didn't quite work as the migration program seemed to be recreating that file whenever I ran it - and even when I removed it immediately after it was created I still received the error.
So flipping that logic on its head, if it is a old fashioned SY_System.m4t it wants - that's what I gave it. I edited the one it kept creating in the windows folder to look like one from a Standard/Advanced system with the same version number as the live system (5.00.4). With that in place it got past the spot of the error and asked for the Administrator password. Problem resolved I thought, then it said it couldn't find SY_Company. Same deal as with SY_System in that it was in the SQL DB and looked fine, only this time it was not in the MAS_SYSTEM folder. I recreated one manually anyway, and even though I worried about possibly creating a scenario where I might be chasing my own tail trying to create many system files, after SY_Company.m4t was in place it gave me the list of companies and seemed ready to begin the migration. On a bizarre twist; I made those changes over 2 days ago and even though I asked the client to stop the service on a server that he has denied me access to he has neither done it nor responded. As I'm sure many of you know the migration won't run if the service is running. Sigh.. Onward through the fog.
Oh, one more note of thanks to Alnoor. I had another client I just happened to be doing a re-migration for from 4.40 Adv to 5.00 SQL and received a message that ""G/L Options is missing"". Sure enough I found an AR_Options file sitting there taunting me in the ARxxx folder. Removed it and all was well. Sorry to be so loquacious, but I thought it was important.