[Too Many Projects]

With the, more complete, history on this, I'm beginning to think it may well be an internal issue. Steel bushings and new shifter eliminate a few of the possibilities. Could still be a loose arm, stop bolt nut loose and allowing the bolt to work it's way down or linkage out of adjustment, but getting worse with time/wear and with the same 3rd gear issue from the past, just seems to lead me to the hub/slider assembly, or another gear problem, now with the engagement cogs.
Talking with the builder may give insight, if he can recall, or have a record of exactly what he did when the gear was replaced.

Pulling the side cover will give a visual of the gear cogs, but they are not the primary component of keeping the slider engaged. Yes good cogs that aren't all rounded and chipped do help, but the keys (dogs to many) in the hub have that task as well as the fork springs and levers in the cover. The keys are under tension from a large "C" spring under them and between the keys being worn from use and the springs occasionally breaking, they are the main reason for popping out of gear. Broken springs and worn levers in the cover can add to the problem.

If you do remove the trans and side cover, moving the slider to second gear should have a slight click sound and the keys pulling the slider into position the last slight bit. You'll probably have to move it a few times to get the syncro ring and gear cogs lined up perfectly to "feel" the keys engaging. If you don't feel/hear the same positive engagement going into 3rd, my bet would be on the hub/slider assembly being an used component that is now worn enough to not hold the slider in place tightly enough.