Like the lathe, nice! the milling machine is a god one too! It is odd about the lathe gearbox, and on the face of it, if you are pushing the lever past the detent position to make it engage properly, something is loose. Just a thought, would a partially sheared key on the change shaft mean that the dog was going too far one way and not far enough the other? It certainly is a conundrum, Next question is can you get the selection mechanism out without taking the shafts out? If you can, all well and good. So what is going on here? are you resurrecting a disused machine shop, are you going in to business or is it just a hobby. Some general pics of the workshop would be interesting, how long did you say it was since it was last used?
Unfortunately I have had the unpleasant job of repelling a rat attack from next doors chicken coop, they have got into the roof of my workshop. I have blocked up the holes, re decked the damage on the roof, tomorrow I have to finish off.................then start taking down the insulation (polystyrene) between the joists to see if they are still there......Oh Joy, I'm so looking forward to my very own room 101 experience.
Phil