Reassembling the calipersAfter destroying one of the seals, I found the answer on Youtube.
Parts are lubricated with brake fluid first, then the square seal goes inside the caliper. That's easy enough.
The trick turns out to be sliding the outer seal down to the bottom of the piston, so it hangs down a little.
Tuck the seal into the slot in the caliper, then ease the piston through it. I rotated the seal to get it entirely into place.
None of the pistons could be pushed into the caliper without a c-clamp. Once all the way in, the upper seal snaps into the piston.