Thanks to you, pch300, I think I'm going to do this repair myself. I have been thinking about the project, and I believe I have come up with a winning idea on how to ensure success with avoidance of rubbing of voice coil.
I would take all your suggestions, essentially, which are superb; thank you!
But, in addition, when I got to the part where I would secure the outer rim of the surround to the metal basket, the thought struck me, why not use some painter's tape, or similar, to temporarily anchor the surround's outer edge, then play the speaker to assess for rubbing? If it rubs, I move it and reattach with tape. The tape should not damage the new surround, and it can be moved at will. In that way I should be able to then work around the bottom of the surround with glue, removing the tape locations and ensuring the proper position of the surround. I can also mark the edge, as you suggested for extra caution/precision.
Obviously, I do not want to crank them up in that condition, as the tape might pull on the driver paper. Then again, I have bigger problems if the surround anchored to the paper pulls away! That had better be right! One has to use some sensibility. I could even, perhaps, use some narrow weights of some sort to place on the surround as an anchor. I would be able to find something suitable.
I think I'm going to remove the drivers baskets today from the cabinet, and turn the drivers over to settle the one spider that's sagging. I also can begin to work on replacing the wiring and posts, which are antiquated and by today's standards poor.
Sounds feasible. Ideas, concerns?