OK, I finally got to watch your video! Got a new computer. works much better...
The side-to-side and wobble on the far right 5th gear is at least twice as much as on any F2 or K7/8 gearbox I have on hand now. They are all in the .5mm range, even in the K4 box I have.
Here's what I am wondering: if this engine case was cut a bit too far away on the bearing side of the 5th gear, it lets the gear slide away from the moving 4th when shifted. This is where I have seen Honda shim the far side of the 5th gear back toward the clutch side with thin(ner) shims. If they got lost once when the mainshaft was out, that may be part of the explanation? (I don't know the history of the tranny?)
Evidence of this is: that one chipped tooth, which shows approximately 1.5mm engagement before the clutch locked up, then chipped off the tooth when the clutch locked back up. If the 5th gear wobble on the inner bushing is sufficient to let it tilt non-parallel to the others (i.e., no longer at right angles to the shaft), then only 1 or 2 teeth get loaded.
Here's the original source of this issue in these later engines: when light oils got used, the cast-iron bushings (like the one inside this 5th gear) take a beating. After their Parkerizing wears off, they can have twice the nominal clearance inside, letting them tilt quite a lot. The "wobble" I see in your video surre points toward this being the issue here.
Most of the engines before the K4 had bronze bushings inside of most of the gears. I won't say "all" because I have seen mixed-metal trannies on occasion on apparently virgin engines, and I have seen bronze in F3 engines after seeing 100% cast-iron inside the F2 (which is one of the ones I now have). So, it's hard to know which way they were building them?
So...what to try next: I don't think I have any "junk" trannies, as most of mine are destined for engines I am building. I have a bottom end out in the shed, though, that might supply some parts? I think it is a K6 or might be a K7. I'm wondering about subbing in a different bushing on that 5th, to see if it tightens things up?