The little wedge (as you call it) is a stop for the pa rim center disc. Once you have all your wedges out the stop, odd one with the little spring, sits in the track and locks it so when you are spinning the wheels out or in it don't over shoot where you want them set at.when spinning the wheel disc it will stop at the lock and the rest of the wedges will be lined up. I should add that it is not needed if you are going all the way in or all the ay out cause there are stops at each ends so you don't spin them right off the rims.
Adjusting the rim is done while on the seat and running the tractor in forward or reverse and braking each wheel. Trying to line them up without a stop is a real PIA cause you wind up over shooting it either way.
The system IMO works quite well. One of the problems is that when farmers set them for cultivating they got locked in place for 50/60 yrs or so. If this is the case than you will have to clean/scrap/sand the edge so it moves freely in the track. Tracks also must be cleaned. Your operating manual will show some diagrams on this.
Kirk