Got the one (bad) side done this afternoon.
The parking-brake-cable assembly was the worst part. The cable housing ends in steel cylinder which is pressed into the caliper body.
It should pull right out, but after 17 years was rusted in place. After fighting with it for quite a while, I did a search for the issue. There was a helpful thread on Mazdas24/7 where the OP was dealing with the same thing.
Those from winterless climates didn't understand the problem.
Those from the rust belt did, and said that the only way to remove the parking-brake cable is to sacrifice the caliper housing by cutting relief slots.
That looked better to me than cutting the cable, so I got the grinder out.
Success! I'm beat, the other side (which is still working fine) can wait for another day.
Yes, I applied lots of anti-seize when installing the cable into the new caliper. I can't imagine anyone ever removing it, but who knows?