Ok, Glen and I flushed the brakes but after lots of testing it became entirely clear exactly what's going on.
Pull hard on the lever, and the brakes are solid!
Pull hard and keep holding, the brakes are solid!
Pull moderately and hold, the lever comes in and in and in and in very slowly until it hits the bar, then you can ROLL THE BIKE with the lever all the way to the grip!
We suspect there's a faulty seal, probably in the brake master cylinder piston, or possibly in the caliper piston.
Our theory is that when low to moderate force is applied brake fluid is slowly able to slip past the faulty seal. When more force is applied the seal spreads under the pressure and properly seals against the cylinder wall.
There must be some mechanism for the "slipped" fluid to return back into the system, because as soon as you release the lever brake pressure returns immediately.
Off to mechanic tomorrow, don't have time to go pulling stuff apart at the moment.
It's totally mystifying to see the lever come all the way in ever so slowly, and then roll the bike with the lever all the way in, then get full pressure straight back on the discs again.