I still cannot get the lathe chuck to hold the 1.5" OD tube. Next step is probably disassembly, cleaning, and reassembly. On the plus side, I found a source of 1.259" ID 1.375" OD tubing, so no need to do any turning. The downside is that I still need a step to prevent the tube from falling through the base, and there are only a few threads to hold an 8-32 thumbscrew in place to prevent eyepiece motion.
Solution: Machine a sleeve about .25" long from that 1.5" OD tube into which the 1.375" tube slides. (Such a short piece should be held adequately by the chuck, and I will be boring the inside, not turning the outside.) Glue with epoxy to hold in place. Now I have .25" of aluminum to hold the 8-32 thumbscrew.
No need for epoxy; I bored that .584" long piece of 1.5" OD to a diameter where it would just barely press onto the 1.375" OD tube. Then I tapped it for a 6-32 knurled head thumbscrew (which I seem to have bought 10 of them, some years back). I also bored the 1.259" ID tube just slightly larger so that all my eyepieces slide in, and only the thumbscrew holds them in place.
I had thought of making a brass compression ring to prevent the thumbscrew from marring the barrels, but this is a plastic coated thumbscrew, so no need. Those brass compression rings are a real pain. You have to excavate a shallow (.050") channel with a reverse rake boring bit, then cut a very narrow piece of brass to fit in the channel.
Because the OD of most of the new tube is 1.374", I am making a new base with a 1 3/8" hole. That is mostly waiting for the slotting program.
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