I had a similar problem with my old 125cc, it kept making the grinding noise in 3rd gear "only" and also kept jerking as if the sprocket was slipping, like yours seems to be doing. At first thing I though it may have been the chain slipping off one of the sprockets, but soon realised that it was a little bit more serious than that.
I also bought a new engine to solve the problems a 140cc (which really does go hard for a stocker), but it only took me a month to kill that gearbox too. I did find 2 meshing tabs floating around in there, off 3rd gear, which eventually found there way into the other gears and seized the box, while is was doing about 50k's. I have new internals in there at the moment and I am about to rip them out and get them back cut and heat treated for extra strength.
Hoping that the problem might have been as simple to fix, I pulled apart my 125, but could not find any broken parts and did not know what was going on for a while either. After look at how it all operated for a while, I soon realised that it was not moving the shifter fork, up far enough on the drum to mesh third gear propel. when I had a closer look at the meshing tabs (technical name) on those two gears they both were polished like they had been rubbing. also after taking the drum out, I could clearly see that one of the shift forks was bent and had worn down the small tab on the end.
I ended up heating the fork (in a vice) and then gave it a few hit with a big hammer until it was kind of straight, I Then welded on a new tab and file it all down to specs. I deliberately bent it back past square to help get rid of the problem, but when it was all back sitting in the case it still didn't mesh as well as it should have, so I then ground down the brass washer in between them to improve the problem and then dished the outer washer a bit more to get rid of play on the shaft.
Anyway I hope this helps, I might not be the same problem, but It does sound very similar to what yous is doing. If it is it may be a lot easier, to try and purchase a new shift fork, instead on trying to repairing the old one.
My motor used to pop out of gear all the time (wont be now) and I used to get the shits with it and try to kick it back in, so that is how I probably bent it in the first place. But I have a feeling that a lot of these boxes don't mesh 3rd as well as they could...So it doesn't take much to trigger the problem. I could be very wrong though.
Cheers Matt