Vincent, your mention of "side play" caught my eye. How are all the shafts and bushings?
Five years ago I overhauled/restored my 1944-vintage Logan 820. Although completely operational, its maintenance had clearly been neglected. All the gears were fine. But the carriage and QCGB had bad wear on bushings and shafts. In particular, the front shaft in the gearbox (the one the two gear selector arms slide back and forth) was badly worn. Most of the bushings were worn enough that I replaced them all and I made new shafts.
This was my "Welcome to retirement project", it kept me busy for over a year. I don't remember how many times I had the gearbox out and completely disassembled. I took it apart to assess it, take measurements and make sketches of the shafts, then reassembled and installed it so I could use it to make new shafts. Then again tear down to install my homemade parts and new bushings, and once again reassemble.
That QCGB slider shaft was so worn, I decided to improve on the original and add bushings on the gear selector arms where factory design had been steel-on-steel (cast iron?). That was a long risky operation. If interested in details, look back to my long series of posts, "Greg's Logan 820 Restoration".
Greg