What is this probability of subjective body-jump actually a probability of? We could set up various Sleeping Beauty-like thought experiments here. Supposing for the sake of argument that I'll live at most a natural human lifespan no matter which year I find myself in, imagine that I make a backup of my current state and ask a machine to restore a copy of me every 200 years. Does this imply that the moment the backup is made -- before I even issue the order, and from an outside perspective, way before any of this copying happens -- I should anticipate subjectively jumping into any given time in the future, and the probability of finding myself as any of them, including the original, tends towards zero the longer the copying machine survives?

As long as you correctly anticipate that you will give the machine that order, and that it will carry it out as stated, that sounds right to me. I'll bite that bullet without further qualification. :) Same with the original question about the duplication machine.

What is this probability of subjective body-jump actually a probability of?

I'd unpack the question "What is the probability that my consciousness will suddenly jump into the new body?" as "Of the agents that I currently know to have a mind-state identical to mine, what fraction of them will have an experience that feels like suddenly switching bodies?".