Toploader pops out of third and fourth

[Jac Mac]

The bolt you removed is a travel limiting bolt that prevents the shifter from 'over reaching' on the gearbox internal elements which can cause damage to the internal shifter rails if left out for a long time and the shifter is used aggressively. Did you use the alignment pin when setting up the shifter rods?

Attached pic shows the detent cover bolt, this is the only detent that is outside box, all others are internal. From your description check this bolt is tight first, if that's OK remove and check the spring is correct length and or not damaged as per my earlier posts for motorhead. If everything is OK there and the shifter assy is operating correctly then the next option is the possibility that the small hex set screws that locate the shifter forks on the internal rails are not tight. Think you will find issue is shifter alignment though.
What is the 'white plastic' looking rod hanging down in your pic behind the 3/4 shifter lever. I also enlarged your pic of the shifter assy, It looks like you have the basic shifter rods quite likely with lots of bends like the pic above.... shift quality can be greatly improved by using straighter shifter rods and rod ends for accuracy... the setup you have at present 'looks' to have enough free play to allow misalignment to occur in the shifter assy which would cause problems moving across the neutral gate from 3-4 and 1-2 positions.... PS, the pic I used is NOT a good example.. too many bends

To adjust that rear stop bolt you had removed......Screw bolt with locknut loose on threads back in a couple of turns Put shifter in third gear, tighten bolt in until it just contacts the lever in shifter unit ( you will see the 3-4 shifter linkage start to move out of third gear ), back the bolt out again by one whole turn then tighten the lock nut. There should be a similar bolt on the front face of the shifter, apply the same procedure to it with the shifter in fourth gear.