Bad brake calipers?

1989 4WD pickup.
With engine running, I push down on the brake pedal, after a little travel I get some resistance, but pedal keeps sinking a couple of inches, then gets hard. It feels like fluid is bypassing somewhere.
I thought this was a symptom of a bad master cylinder, so I replaced it, no joy. Yes, I bench bled it, then I bled the lines different ways. I tried gravity bleeding, pedal bleeding, and pressure bleeding from the wheels up to the master cylinder. It's hard for me to believe that I didn't get all of the air out one way or another, but I suppose it's possible. The pedal doesn't feel like air in the system to me. My experience and understanding is that with air in the system, the pedal can be pumped up, and stay pumped up until the pedal is released.
Also, with the engine not running (no vacuum boost), the pedal feels a lot better.
If I pinch off the flexible lines to both calipers, the pedal gets rock hard with very little travel. It makes no difference which end of the flexible lines (the end closest to the caliper, or the end closest to the master cylinder) same result. Pinching off either caliper improves the pedal feel considerably, but still a little pedal sink. I know this indicates that the problem is downstream of the pinch point, which only leaves the calipers, but I can't wrap my brain around how a bad caliper can make a pedal feel like a master cylinder is bypassing.
The slide pins were pretty rusty, but brake pad wear was pretty even, and I cleaned up the pins. Brake pads had about an 1/8" of material left on them. I replaced the pads hoping that it had something to do with the caliper pistons being so far out, new pads didn't help, in fact it might have gotten worse.
All caliper pistons seemed to move freely.
Both rotors had places where the pads had not been contacting them, it was on the inboard side of both rotors, about 40% of the inner part (closest to the axle).
The LSPV has been removed, and a manual valve installed.
I think I'm down to just putting new calipers and rotors on it, but I would like to pinpoint the problem and understand what's going on. If I put new calipers and rotors on it and still have the bad pedal, I'm going to go ballistic.
Again, I can't figure how bad calipers could make the pedal feel like it does.
Anyone seen this?
Anyone have an idea how bad calipers could make a pedal feel that way? A caliper seems like a simple device to me, pistons move out, pistons movie in. As far as I know, there is nothing inside a caliper to internally leak or bypass, it can only leak externally.