Thanks, 87nasupra. I was afraid it's the ABS unit. It has to be, by process of elimination.
Yesterday, I swapped out my booster for a slightly newer one. Neither are rebuilt units. With both out, I compared the freeplay in them, and they were both the same. The input shaft (pedal side) moves about 1/16" before the output shaft moves. That certainly isn't enough for the amount of dead travel my pedal has. The output shaft of the replacement booster was 0.025" longer than my old one, but I had to go with it because the adjustment nub wouldn't turn.
I guess I look for a new ABS unit next.
Aren't there 3 solenoids in the ABS unit? Which is RR? That suggests "right rear" to me, but both rear brakes are controlled together.
Asterix