Hi dmcneil. That would often happen to my dads GMC if you weren't careful when shifting into reverse. Only difference is that his transmission would be stuck in two gears at once. In order to get it unstuck you'd have to take the shifter out of the top of the transmission. Then you'd reach in with a prybar to the shifting rails and pry them back into neutral. It was all done by feel, but you might be able to look down inside with a flash light to see the problem. It could be too that someting slipped on the rails. But sounds like what ever is wrong you can fix by just taking off the top of the transmission, which isn't too bad of a job. Good Luck.

1948 Chevy 6400
1964 Chevy 1/2 Ton