Sinking brake pedal

Anyone seen a sinking brake pedal due to a bad booster, or bad flexible lines?
Problem is only with engine running. Pedal feels great with engine off.
Booster passes all tests I know to do.
Pedal has some initial resistance at normal height, then slowly sinks a couple more inches.
New calipers and master cylinder. Pinching off both front brake lines prevents pedal sink.
All brakes except right rear can be locked up on pavement. Quite certain rear right does not lock up because of recent contamination from bearing seal failure. Shoes are still hard, I will clean, or replace if necessary.

 

Could be the booster, the master cylinder or air in the brake lines. How about a little more info. year of truck, miles, when was last brake job, did you do the brakes or did a pro do them?

 

1989, 4WD. 160,000 miles. I've had a problem with poor braking for a while, I decided to address it recently since the rear right bearing seals leaked gear oil into the drum area. I pulled the axle and took it to a shop to get the outer seal replaced.
I do most of my own work. The last brake job was years ago, I don't remember how many. I have not put many miles on it for years since I worked away from home for the last 15 years, and I have 4 vehicles. The front pads had 1/8" of meat left, the shoes are like new. The shoes and pads probably were not changed at the same time.
I've bled, and bled, and bled. I tried gravity bleeding, pedal bleeding, pushing fluid up from the wheel cylinders to the master, and vacuum bleeding, no change. It's very difficult for me to believe I have air in the system.
It's also hard for me to believe the master cylinder is bad since replacing it didn't change anything, and brake pedal feels real good with engine off.
The problem is only with the engine running points me toward booster, but it held 15" of mercury for an hour last night. I found a video that shows a test for the booster poppet valve on Youtube community college, I tried it and it passed. I hesitate to spend $225 for a booster until I'm pretty sure it will fix it. I was skeptical of the problem being the calipers, but pinching off or plugging the front lines pointed me in that direction. I'm trying to find a known good used booster to swap in for troubleshooting.
I put in new calipers and pads since I started this job, the rotors are original, as are the flexible lines. The LSPV was removed and a manual valve installed by the master cylinder. Plenty of meat on the shoes, drums are in good shape. Pinching off rear flex line doesn't change the symptom. Installing plugs at bottom of front flex lines gives me a hard pedal as well.
After I replaced the right caliper, I put a steel block inside and tried the brakes. No change, which I think eliminates anything to do with the rotor and axle. Left side flexible line was plugged at that point.