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But Zeno himself meant to deny motion?

I strongly doubt it, cornelis.

I think what his paradoxes show is that, if you load an unfounded/incorrect assumption into an analysis of a problem, you could find yourself "proving" something that isn't true. The incorrect assumption in these cases is that time is divisible into discrete units. Thus all the results obtained contradict the types of results that we would expect to obtain on the basis of direct observation, knowledge, and experience.

Zeno's logic wasn't faulty. His "trial assumption" was faulty. And I think he knew that. That was the point. He probably took some pleasure in the effects his paradoxes had on people who engaged them, perhaps thinking it would be difficult for many if not most people to spot the fundamental problem that lies at the root of their construction. Of course you're right: "puzzles can work within their own definitions." Whether those definitions have anything to do with objective reality is the real question.

I think Lynds, if anything, wants to thank Zeno for showing how our own mental constructions of methods to solve problems can be self-defeating, leading to absurdity. I get the sense that Lynds goes Zeno one better: That if time were actually divisible into discrete units, nothing could "move" at all.

Merci beaucoup for the primer. It would be news to me that Zeno suggested correct premises (we have no record of them). If any are supposed, they should answer to the Parmenidean notion of the identity of immutable being and thought. But that is a different problem than determining whether we are speaking of spatial infinity, temporal infinity, mathematical infinity, divine infinity, epistemological infinity. To solve one of these for the sake of Zeno is tanking on a supposed controvertability of the elements of different puzzles.

I get the sense that Lynds goes Zeno one better: That if time were actually divisible into discrete units, nothing could "move" at all.

Not necessarily. Things could occur by jumps. There might be a system where one measures the position of a particle and "later" does another measurement for which the particle is somewhere else. (This describes discrete space.) Were time discretized, one could look a the "fundmental clock" and only see discrete units. There would be no experiment that could give a result that was between one tick and the next. If the resolution were fine enough, all of ordinary dynamics can be recovered (and there would be no obvious experiment that could distinguish a really fine discretization from a coutinuous theory). There are discrete models (used in numerical analysis) where energy, momentum, etc. are exactly conserved. The accuracy of the discrete mechanism is roughly of the square of the finest division.

Additionally, time divisions could be only countable but dense rather than continuous. This would recover all of dynamics easily because the Riemann integral is sufficient for such cases. (Continuous time requires a Lesbegue integral. I'm not sure there's an experiment that shows one rather than the other to be "correct.")