Geeez, I'm such a dolt...
Actually, your "Select Point" option is exactly what I want in this case.
I rejected "Select Box" initially in this case, because I couldn't put a box around the points I WANT to move without also selecting points I didn't want to move. However, what I *really* wanted to do is just move each point into the middle of the path that I know I was walking on... which is exactly what "Select Point" does.
I don't know *why* I am so easily confused these days.
Anyway, once again TopoFusion proves itself to be not only an ideal tool, but the only easy-to-use tool for the job... Thank you for your help.
There *is* another issue that I have with TF, relevant to my current requirement, but it's a different topic, so I'll post it separately.