All finished, put back together, and running well! I took it apart in the first place because I wasn't happy with the stem engagement-it turned out that some watchmaker(watch butcher) in the past had filed the "square" on the stem-and very poorly at that-causing the problems I was having. Fortunately, I was able to scavenge one from a parts movement, and all is well. I also put the case stem in the lathe and turned the "shoulder" back a little bit so that the catch would release the front cover better than it had been.
The result is that the cover opens perfectly, and winding also works perfectly with none of the slipping problems I was having before. I need to run it for a few days and let it "settle in" before trying to time it(pretty standard practice for a freshly serviced watch), but overall am happy with how it turned out.
This is an 1872 model Waltham. The case is gold filled, and these are-surprisingly-quite a bit less common than karat gold cases. Coin silver cases are also fairly uncommon for these, and sterling cases are downright rare(I have an English-market sterling 1872 model case, and have been offered mind boggling numbers for it considering what it is). I think this all has to do with the fact that the 1872 was designed and marketed as a higher grade watch-the "Royal" is actually the lowest grade movement.
I hadn't done any watch work in a while, and it reminded me of how relaxing sitting down at the watch bench and tuning out the world around me can be.
What a lovely elegant watch, and what a wonderful story to go with it.
Will you wear it, or otherwise use it on a daily basis?