All right everyone .... the problem was, of all things, an issue with the pump impeller slipping on it's input shaft. The bond between the rubber impeller and the shaft it is mounted to failed and allowed impeller slip on it's shaft - causing a significant reduction in pumping capacity (diminishing it to zero in my case).
Here's what I did to diagnose the problem. These checks were done with the outer cover of the washer removed and the lid switch jumpered out so that I could 'see' the internals of the machine during the cycles.
1) Used an Ohm meter to check the integrity of the motor. The procedure is described at the following website: http://www.repairave.com/washerrepair_wp...
My motor ended up being a 3 speed model and all the resistance readings checked out perfectly. The motor was in great shape.
2) Checked the RPM of the motor, clutch drum and washer basket during all the cycles of both a Regular and a Heavy Duty wash. The Regular wash is supposed to be a slow motor speed for agitate portion of the cycle and high speed for the spin portion. The Heavy Duty wash is a high motor speed for both the agitate portion and the spin cycle. I used a laser tachometer using a strip of reflective tape on the 3 measurement points. One on the motor shaft - between the pump and the motor - to read the motor RPM. One on the outside of the clutch drum to read the output speed of the transmission during the spin cycle and one on the inside of the washer basket to read the basket speed. Here are the results: Motor high speed is 1760 RPM, motor low speed is 1175 RPM. The clutch drum speed was 649 RPM when the motor was on high speed in the spin cycle. My drum speed as only at 165-300 rpm when the basket was not draining properly (still had water in it). The basket speed is supposed to be the same as the clutch drum speed - 649 RPM - when the washer has properly drained and the spin cycle is at least 30-60 seconds underway.
3) I timed the draining of the basket at both the wash and rinse cycles. I learned that the pump is timed to run for about two minutes (120 seconds). I also learned that the motor is running at high speed - 1780 RPM - when the water is being pumped out of the basket. If the water doesn't drain in the allotted 120 seconds and the motor is running at it's proper speed, then there must be an issue with the pump itself or the hoses downstream of the pump. In my instance, the pump only evacuated about half the water in the 120 seconds that the pump ran. Knowing the motor was in great shape and that it was running at full speed - 1780 RPM - this convinced me to double check for constrictions in the drain hoses.
4) I removed the goose neck at the end of the drain hose line and ran a stiff bristle brush through the curve of the goose neck and all sorts of crap came out. I cleaned all the drain hose (from the pump to the gooseneck) and reassembled the washer.
5) I ran a few loads through and found that the time to pump out the water was greatly reduced. All the water was pumped out in 85 seconds and the washer was empty for the last 35 seconds of the pump cycle. Things looked encouraging.
6) The speeds during the subsequent spin cycles were phenomenal. The motor spun at full speed 1760 RPM and the clutch drum and washer basket ran at the same speed - 650 RPM. All was well in the spin cycle.
7) After a few days of running, the "water left in the tub" phenomena was rearing it's ugly head again. I re-checked and re-cleaned all the hoses. All was well. I checked the motor speed at the input to the pump. All was well. The motor was spinning at 1780 RPM. You could actually hear the pump 'slowing down' but the motor driving the pump was not slowing down. I pulled the pump from the machine and turned the input shaft by hand. The impeller turned with the input shaft. I then 'jammed' the impeller with a screwdriver and once again turned the input shaft. Sure enough, the input shaft turned and the impeller was stationary. The impeller was slipping on the input shaft. I'm not sure how these two items (impeller and input shaft) are bonded to each other but this bond obviously loosened. Time for a new pump.
Here are a few more websites that I referenced in the journey of this repair: