Well, I’m not sure how to give you confidence, but I can tell you that as long as you don’t manhandle the parts, you really can’t ruin anything beyond repair. If the game doesn’t work, you’re not going to get any enjoyment out of it.
If you think the mechanism is free enough to work, then you should focus on the 2 switches that I outlined. If they are dirty or not making good contact, it would cause the problem you described. It could also be a bad solder connection at the wire tab (because you report that it works with the playfield up). If you need help with the wire colors, they are in the schematic, and I can point them out.
If the race unit step up coil is getting energized and not stepping up, then it’s a mechanical issue and you’ve got to clean the unit. It’s really a process of taking lots of pictures, carefully removing the springs and fasteners and keeping them organized, cleaning, and reversing the process. Fortunately, there is a ton of documentation on those Williams steppers, lots of pictures online, and lots of people who can help you out if you don’t put it back together right.
Your other option is to find a local service guy or pinsider to make a house call.
Dave