Mine was doing about the same thing, (94, 4.0 m5r1). I put in the kit from The American Powertrain Warehouse online, the bearings seemed to be high quality, all new synchros, needle bearings, gaskets. Cant remember what part number, but they claim they don't use the cheap Chinese bearings. (got about 5k miles on it since rebuild and still quiet)
My input shaft had a little play before disassembly, but I attribute that to the apparent cheap rebuild from the PO. (used the china special stuff). What you need to watch out for are the bearing retention plates, they wear and will offset the final shaft endplay. The easiest check for this is to put the tranny on end and see if you can pull up on the output shaft, it shouldn't move. From what I understand these usually need to be replaced as well (I got lucky and mine were fine, PO got something right I suppose).
As far as side to side movement, I would think that would relate to sloppy bearings, but I don't build these for a living so I'm not sure.
I never did find a technical manual on it either, I looked and looked, eventually I just compiled a mess of different pages from forums, aftermarket part sellers, and snippets from some mysterious tech manual (so I know it exists) If I can find my notes all let you know.
Hopefully some others will chime in, but personally I probably wouldn't replace the shafts unless the teeth look worn down (mine looked like new after 205k miles, to give you an idea, although you could see nearly microscopic wear) However, I don't know how much play you had, or how loud the noise you heard was, just throwing my thoughts out since it seems nobody has picked up on this yet.