OK. First off, apologies if I have missed the answer somewhere but everything I have read has lead me to a different issue. This is a different grinding issue that what I have read so far. The car is at school with my son but he is babying it for the next month due to lack of options.
The car shifts normally in all gears but either 3rd or 4th. Actually there is no grind in any gear going in. But when you let the clutch out it will come out of gear most times. Depending on how we adjust the shifter we can get it to either work in 3rd or 4th, but not both at the same time. If you "slam" it into the suspect gear it will hold fine. Once it is in gear it stays.
My conclusion is that the transmission is simply not fully engaging the gear and depending on how the cable is adjusted we can choose which gear is not fully engaged. There is a grinding if you are resting your hand against the selected gear but not really pushing on it. The recommended shifter adjustment does not work at all but by shortening the 3/4 cable we can get it to work in 3rd. This lead me to the loose rivet issue, but that doesn't seem totally correct when comparing to the symptoms I read. Another thread pointed to the shifter itself, but the other gaits work fine, sooo....????
What I am looking for is a reasonable suggestion as to what to look for next. From past experience it sounds like something in the shifter forks inside the transmission but it would be nice not to take the transmission out of the car only to find that the problem was somewhere else. In reality it seems like the problem is more play than I would have expected only from a shift fork, but not that familiar with this gearbox.
I hope I have described the issue well enough to answer many questions in advance, but please ask questions and make suggestions. If you have had this exact issue, I would love to know more.