O.K., I finally figured it out! What I just couldn't understand was how a problem with the water inlet would cause the dishwasher to leak in the latter third of the DRAIN cycle but, now I know! After pulling the dishwasher almost all the way out (electrical wiring wouldn't let me go any further) and pulling off the insulation blanket, I noticed that the water stains appearing to emanate from the bottom of the water inlet on the side of the unit were actually coming from farther above (left, rear top-of-side). So, I took a flashlight and shone into the upper back corner of the dishwasher cavity (where the drain hose heads towards the sink drain) and it looked like there was some scale on the outside of the corrugated plastic hose right where it had been forced to do almost a 90 deg angle down towards the floor. Seeing this, I decided to disconnect and then pull the drain hose and, lo and behold, the hose was cracked between five of the 'ribs'!
Now it all started to make sense - this is what was happening. As the unit began the drain cycle, water would leak from the hose into the insulation blanket that it was immediately adjacent to where, after some period of time, the blanket would become locally saturated and water would begin to drip down the side of the cabinet and the unit where I would dutifully catch it or mop it up. This would repeat itself every time the dishwasher would go into drain cycle (3 times per use). So, now I knew I needed a new drain hose for a 23-year old dishwasher, which tuned out not to be a trivial task. Reliable Parts told me that the best I could hope for was a 'universal' corrugated, plastic hose. The one I needed had a 1/2" connection at the dishwasher end and a 5/8" connection at the sink end and was 7' long. After exhausting all of the sources I could think of, I decided to buy 7' of 5/8" I.D. black rubber drain hose and put a short, plastic 'sleeve' inside the dishwasher connection end (the fitting there is only 1/2") and tighten the hose clamp snug.
All is now back together and we are just waiting for the dishwasher to fill up with dishes before we give it a try. Wish me luck!! Being a 'concrete sequential' kind of guy, I need to be able to explain observed behaviour in order to validate possible causes.