The F2/3 gearbox can be...cranky...at times.
Here's some things that might help your search:
The K0-K3 shift drums have a slightly smaller OD where they exit the side case, making them sloppy. Their shift drums also had wider grooves and the shift forks had narrower-diameter dogs in those grooves, letting the assembly rotate more easily. Unfortunately, this also causes less-deep dog engagement, and the first casualty of this is the 2nd gear's dogs, which wear on their ends. After a while, this causes the 2nd gear to jump out or press against the L fork until it wears or bends, and the 2nd gear becomes unreliable.But...this also makes the 3rd gear MORE reliable, pressing those dogs deeper by the amount 2nd gear has lost it!
It's a bad news, good news sort of thing...
When "the cheapening" occurred in the post-1975 bikes (and some of the K4-5), the first casualty was the bronze insert bearings in the tranny (they became much cheaper iron-alloy type). The bikes that suffered the most from this were the higher-powered "F" bikes, especially if 10w40 oils were used (because of the [in]famous "Jinglish translation error" from 1973's Owner's manuals). The result was: the iron-alloy bearing inserts galled, making the gears stubborn about moving on the mainshaft or countershaft during shifting. It sounds like one of your trannies (not sure which one?) also got mis-assembled at some point, if the oil holes in the insert were not lined up? This can also gall the bearing itself on that insert, which makes it drag. So can the backward circlips and thrust washers...
About this time, Honda seemed to lose their more experienced engine assemblers in the SOHC4 shops (maybe they were going to the CX500 or Honda cars?), and the trannies started coming out with snap rings backward, thrust washers backward, and mis-set spacers (especially on 5th gear, mainshaft), starting around 1976. In the meantime, the shift drum had changed, first in the K3 late models, to have a tighter fit in the groove, with deeper grooves and longer fork pins, and "wider" Neutral ramp for a more-positive Neutral 'find' when the engine is hot. This increased the side forces on the shift forks for the 1-2 gears and made the position of the "C" fork critical: if the "C" is bent even slightly, it stops shifts to the 3-4-5 set, or at least makes them stiff.
I have taken apart several post-1976 engines and had troubles getting them back together to shift right, several times. Along the way I have noticed things like: the Neutral Switch had to be installed the right way, as it was not quite symmetric. Or, I had accidentally rotated one of those iron-alloy bushings 180 degrees from where it was first located on the shaft where it lived: rotating it 180 degrees again let the gear slide across it easier (this happened when I took the whole tranny apart for cleaning). Or, the O-ring in the "F" engine's Neutral Switch had to be 3mm thick, not the 3.2mm stated in the "sanitized" Honda Parts lists we see today: the older bikes used a 3.2x18mm, unless it leaked, then it had a 3.3x17.9mm instead. The Neutral Switch in the F2/3 cases are often so tight that I've used 3.0x18 or 3.0x17.9 just to get them put back together, and if the O-ring is too small in section, the switch sticks up too far in the case and drags on the shift drum or pushes it slightly off toward one side (then it needs the 3.2x18 or 3.2x17.9 o-ring). The latter causes troubles IF the shaft for the shift forks is not dead straight: they are sometimes bowed in the F2/3-K7/8 engines (for reasons I've never ferreted out...). Then this shaft has to be rotated until the forks slide the smoothest-possible way. Lots of playing around...
Finally, there's the issue of the bent detent lever. This one pops up here and there: the lever gets bent a little either from a poor assembly technique by someone, or a shifting accident, or something? But, the little wheel doesn't sit parallel on the shift drum ratchet detents, so the drum does not shift all the way into/out of the gear selected. I sometimes think this may cause the warped fork shaft, under hard-riding conditions where the 3rd gear would then have strong leverage against the "C" fork, bending the shaft a little, but that's supposition at this point...but, if the gear is not fully seated, and the (iron alloy) bushing is hot from marginal (10w40) oil lube, and the gear is hot from running, the clearance in between them is increased. This lets the gear tilt. This in turn pushes against the fork and reduces the engagement dogs to the next gear, tilting it, also. Then the shift requires a lot more force to make it happen.
One way to find out if this is the culprit is: use thicker oil (20w50, preferably mineral-based like EXL Bel-Ray or Amsoil), run the engine through the gears with the bike on the centerstand until hot, shut it off and come back the next day, repeat, then go ride it. If it gets better, consider using some zinc additive to help the marginal bushings recover some of their excessive clearance and slippery-ness as the zinc attaches itself to the cast-iron material. Over a time, this should help.
I realize none of these are the smoking gun, but these are the things I've found in the F2/3, and some of the K7/8 engines from time to time.
