I promised to write back, so here I am.
Everything is up and running. The known problem that my support dude (very knowledgeable guy, too!) mentioned to me was that Migration can APPEAR to freeze and get out of synch (the two computers showing different times and amounts of data, while one is not moving) when the computers are connected via Ethernet! Wild, right? However, mine was glitching and having trouble recovering because my cable had a flaw. I didn't even bother replacing the cable (though it was estimated as being more than twice as fast as wireless) but upon support dude's advice I performed my Migration over wireless, and it was completed by the time I woke up this morning.
I hope this can help others with a similar problem. One thing that had been recommended to me before I even started was making sure my old computer was on the newest OS. I had been stuck on Catalina because newer drivers were not available for some of my music equipment, but since I was abandoning my old Mac Mini I didn't care any more and upgraded to Ventura. This apparently went a long way to enabling the remaining problem to be solved easily.
Again, thanks to you two, who were right on the money.