How Works the Front Part of a VW Bus Transaxle, Abridged

To recap: one day late last Summer Ludwig wouldn't come out of first gear. The video below, much moreso than the picture at the relevant post, clearly shows both the proximate and ultimate causes for such.

Thanks to Jeremy for the video

After discussing the situation with a local machinist, he installed thread inserts in both of the bracket's mounting holes (it's obvious from the video that the upper one was shot, but the lower one was about to give way as well). Those little tangs you see down in the holes, those tangs are part of the insert and are normally removed after you insert the insert--by knocking them off with a screwdriver. We'd rather not knock two little chunks of steel into Ludwig's gear carrier with a screwdriver, so the tangs will stay where they are. At Amskeptic's advice, the bolts were quadruple-checked against contacting them.

There're the new bolts, mightily (knock on wood) holding that bracket to the body of the transaxle.

Up is right. The abovementioned bracket holds that shaft in place. The gear selector fork rides up and down the shaft (keep your dirty remarks to yourself). The fork itself is linked by an unshown mechanism to the shifter in the cockpit; the driver shifting up there makes the fork move back here. The tabs on the fork push in or pull out those shafts marked 1/2, R, and 3/4, putting the transaxle in gear. 
This transaxle is in neutral, but if the fork pushes in the 1/2 shaft from this position, it'll be in 1st gear. If the fork pulls the 1/2 shaft out, 2nd.

Still in neutral but in position to select 3rd (in) or 4th (out).

Finally, ready to select reverse (out, I think).

Brief pondering helps one realize that for proper operation, the fork's movement must be restricted to movement up and down the shaft, and twisting about the shaft (that's what she said (sorry)). If the shaft isn't held in place by its bracket--owing to the bracket's mounting bolts being stripped out and free to move (see: the video above)--then the driver's moving the shifter up front moves the fork in all kinds of wacky directions, none with the force to put the transaxle in to, or out of, any gear other than the one it was in when the failure occurred.

The next step is to clean the surfaces and glue the nosecone on.