Hah! I just found out what the problem was. Now, I was told that the car had gotten a new clutch just before I picked it up, and a poor installation might have been indicated. Here I am, a few months down the road -- I've been fixing stuff up and getting to know the car better, then last week was the first show for the new car. Once I got home, I decided, since it's a month before the next show, that I would tackle the shifting problem. I used both a Clymer's and the oem GM manual's guidance...
Both manuals didn't mention the metal key you have to remove to get the shift knob off. And both manuals didn't bother to mention that I would need to get under the car to tweek the shift rods. But... by the time I had exposed the shifter mechanism by removing the panel, I found a likely culprit. I thought that there was something that appeared to be kid's breakfast cereal in the shifter area pocket, but when I went to vacuum it up, it hit the canister hard. I took a closer look at a couple of chunks and decided that it was something much larger and that it was broken up or crushed.
I didn't have the "gage pin" the manuals called for, and instead used the drill bit to check for the alignment. It was fine, and the test ride was, too. So I think that for me, the issue I had was foreign object related, although I don't really know how the substance got in there. At least now, I know how to adjust the rods later on, but I think I fixed it for now.