Turned out to be the wheel bearings...
After checking the axle nut tightness as Mernsy suggested (it was tight), I became convinced that the problem was in the half-axle. So I bought a new one from Advanced Auto and put it in, which was an easy job thanks to the Eaglepedia. However, the wheel movement was still there.
So I took the Eagle back to the local garage that had replaced the bearings on that wheel. After much drama involving accusations of lost parts, etc., they replaced the bearings under warranty, which seems to have solved the problem.
I think the local shop was probably in over their heads working on an old car like an Eagle, and probably screwed up the initial wheel bearing replacement in some way. But they made it right (after a little arm-twisting), so I'm not complaining. Just won't use them again.
Thanks to Mernsy and DownwardFlame for weighing in...
JB