This same thing happened to my 2011 Yukon about 2 years after I bought it. I didn't take the seat off though. I don't believe it's the motor. I read somewhere that it may have a round gear which went all the way to the end of a worm gear and the gear teeth and worm gear can't reconnect. I have no idea if this what happened. I went to the local dealer (parts & service) to possibly get a replacement part and the guy said "Sure! Here's the replacement part. It's $660, for the whole seat."
I tried to get him to let me peek at the computer screen and see what the exploded diagram looks like (and maybe get it from a crashed vehicle or online), but those two guys in there are NOT cool to talk to. (Only business I've ever been to where they DON'T want to sell you things, and I ain't talking about this seat part. I'm talking about other parts. I digress).
I you can, please post a pic or two of the motor, gear/screw. You are much closer to figuring it out than I am (because I haven't removed the seat.)