I went on the slope under the house and down to the room where the pump is. THe pump is a good 20 feet below and another 30 feet south of the skimmer basket, and I would say the bend in the pipe where I think the dropped pipe is stuck is a good 50 feet from the pump and through a number of bends. I don't think backflushing from the pump would help. I think it is too far, and since the dropped object is a pipe, there would be very little water resistance. It would seem that the water would just flow through it. IT seems that hooking it would be best, as Zea 3 suggested, but I worry that I might get the dowel or hook stuck in there, or lose them and cause more problems. The drain king was mentioned. I am unfamiliar with this, but I watched a youtube video. It seems that it jets water out under pressure. Would that be okay in the pipe. that might work.
The plumber's snake seems the most feasible. I haven't used one--Once in, would it be able to grab the rim of the dropped pipe so I could pull it up? That is, of course, what I was trying to do with the gizmo I made. I am very leery of doing anything that would make the situation worse, and I am on a small island now and not sure what is available here.
Right now the suction seems normal, so I guess the water is just coursing through the dropped pipe. If the dropped pipe is indeed lodged in the bend where I think it is, it is probably well stuck and unlikely to be able to move further through the bend.
I have to give this a good thinking before I proceed. As I wrote, the pump is back on, the suction seems normal, and I don't think that the dropped pipe will be able to move further down due to the bend in the main skimmer pipe where I believe the dropped pipe is lodged. Since suction is good, I am tempted to leave well enough alone rather than inadvertently cause more problems. Am I being foolish?
This is a great site, I really appreciate all the comments, and am considering them seriously. I really thought I was going to be able to pull the pipe out with the gizmo that I rigged up, but no go. I am not at all well versed in pools, and this has been a great help. I welcome any further comments/suggestions.