From what you say it does indeed look the case that it is for the earlier 'box, and therefore perhaps the stick is right and the jumping out of first is not related to the remote. I appear to have a remote and stick from a Bugeye
There are two different lengths under the ball, but it's not related to the jumping out of gear. You would recognize using the wrong one by the shifter feeling extraordinarily sloppy, especially for example, shifting into reverse - or in your case, being way too tight. I have experienced this mismatch on a couple occasions, and am familiar with the difference in feel.
The jumping out of gear is an issue with the 1st/2nd synchro hub. The outer ring of the hub is the fist gear, but acts like any other synchro hun for 2nd. The inner and out hub hold their position in 1st or 2nd by a set of 3 springs and 3 balls that fit into a detent on the inner surface of the out hub. If the springs weaken or break or in the detent ramp develops wear, the outer ring will not remain in place. Sometimes, these balls can even pop out of their home in the inner hub. Normally, this can cause the hub to lock in gear, but if the spring is broken or is sheared off by the rub retracting, there's not enough tension on the outer hub to stay in gear. This is especially triggered by the change in torque on the input shaft, i.e. removing throttle pressure. It can also be triggered by sloppy bearings and/or too much end play on the input/output shaft.
The cure requires inspecting and rebuilding this hub, and the gearbox in general.