Thanks for the quick reply, Pool-creetin.
For anyone with the same trouble -- I figured out how to separate the piston from the tube (the part with the impeller on the end). Just pull real hard, duh. Then I almost lost the ball when it washed out one of the holes in the center chamber left by pulling out the tube and piston shaft.
Not having any extra-fine sandpaper on hand, I polished the piston shaft with a Mr. Clean Magic Eraser*. That's about the mildest abrasive I know of (and is also great for removing waterline stains, etc). It didn't get out the deepest scratches, but it polished the edges so that they are hard to see. Now it goes in and out very easily. (I also cleaned all the gaskets & seals as recommended by Wolfmarsh, and got all the dead ants out.)
Back in the pool it hung up one time. I shook it a bit while holding it under water. I think that it had air trapped inside as it released a lot of bubbles. It's worked about 10 hours now, but sometime this morning it got trapped on the ladder. I was able to stop that last year by raising the pressure.
For anyone interested in PARTS: :blah:
Parts blowup is in the manual, which you can d/l from polarispool.com. The complete mechanism is almost what the whole shebang costs -- hoses, (Turtle :?

and all. The "Center Chamber Rear'y," Part #6-409-00, is the clear plastic chambers with the short hoses with the jet nozzles attached. One site, poolcenter.com, lists the large O-rings and nozzles separately, but they do not list the Center Chamber Rear'y. Apparently, the inside seals that the piston shaft and Filter Connector/Randomizer Tube ride in are made into Center Chamber Rear'y., so if they need replacement, you must buy the whole thing.
On that one commercial site, Part #6-411-00, Piston Assembly is $21.55 and Part #6-406-00, Filter Connector / Randomizer Tube Kit, is $7.53. Not at that site, but Google Shopping showed Part #6-409-00, Center Chamber Rear'y as low as $39. All these prices are as of this post.