What I noticed was that, even with the handbrake lever released, the handbrake actuator arm on each caliper was well over midway through its travel, so pulling up the handbrake lever only moved it that last 20% or so. In addition, the adjusting nut on the yoke between the lever pull rod and the cable was almost all the way at the end of its travel.
OK, so it appears that the self-adjusting mechanism inside the rear brake pistons was not doing its job. Here's the trick I found and maybe you all know this and it's common knowledge, but I don't recall seeing it in any manuals or forums.
Loosen the adjusting nut on the yoke for the cable to lever linkage so that the actuator levers on the calipers are fully released. Then, sitting in the car, alternately pump the brake pedal and firmly pull up/release the handbrake lever. Do this many times, perhaps for about a minute or two or three. Yes, it gets boring.

After I did this, I found that the rear calipers were pretty snug against the pads, even with the handbrake off. I'm thinking that alternating between the brake pedal and the handbrake slowly moves the adjusting mechanism inside the piston, getting it properly positioned. The key to this adjustment is having the handbrake cable fairly loose before you do this. The last step is to tighten the adjusting nut on the yoke in the center so that the handbrake locks up the rear wheel after 3 or 4 clicks and the wheel spins freely when released. And voila: my handbrake now works as it should, or at least significantly better.
-Bryan