Good news, Bad news...
Well, I found the source of the problem. The 2-3 gear shifter fork inside the side cover of the transmission is seriously worn. There was a lot of powderized metal from the thing that had got stuck in the nooks and crannies of the side cover. I cleaned it all out and put the thing back together, but 2nd gear is still bad.
Now the challenge is to find a replacement part. I usually rely on NAPA for hard-to-get parts for my truck, but they don't carry anything for the GM transmission.
Anyone have any suggestions?