The "slipping transmission" could just be a belt that needs adjustment. My comment above tells how to adjust the belt. Just loosen the hex screw, let the spring put it back into position, then tighten it again. Sometimes it takes a little more fine tuning. Sometimes the belt is so dried out, it needs to be replaced.
I love working on the old Berninas!
There are 2 "nylon alloy" gears in that machine. One is the camstack gear and the other is the vertical shaft gear. They can both be replaced with after-market gears that are pretty good. You can visibly see a crack if it has one. Unless it's the camstack that's stuck with the crack at the bottom.