Thanks all, and the mystery has been solved. The new RAM passed every memory test I could throw at it, and I have a dozen or so of them that I could hit it with. When the RAM came back "clean", I started guessing that it was some form of wait state issue between the GPU and that RAM, since the new RAM is a bit slower than the old RAM it replaced. I consulted the manual for the Diamond Viper VLB video card that is in the system and found a jumper for (a) "Zero Wait States" and (b) "Normal". It was set for zero wait states, and so I set it for "Normal" even though what "normal" was wasn't defined by the manual. However, this change too made no difference.
At this point, my gut told me that this had to be a software issue, and most likely one of those where the Viper's driver was slowly consuming some form of Windows resource , and when that resource was exhausted, the machine would freeze. I tried monitoring free RAM and Windows System Resources, but neither of these showed any downward trend. Still, this just felt like a software issue to me, and so I decided to execute a strategy that has worked for me in the past. When all debugging efforts seem to lead nowhere, stimulate the test system with seemingly unrelated inputs and observe what the output is. This will often change the behavior of the system enough that you glean some additional information that points in the direction of the actual problem/solution. In this manner, I decided to do three things: (1) do a "clean" boot of DOS (no config. sys or autoexec.bat, except for loading HIMEM and EMM386, which Windows needs) and then go into Windows and observe if the freezing behavior changed in any way, (b) disable Windows 32-bit disk access and again observe the outcome and finally (3) unplug the network cable and again observe.
I didn't get past (1). That solved it! After a "clean" boot into DOS followed by starting Windows, Windows remained stable and ran for over an hour before I stopped the test. This confirmed that it WAS a software issue. I guessed some form of conflict between what was being loaded in config.sys/autoexec.bat and Windows itself. I could have exhaustively added things back to the "clean " boot versions of config.sys and autoexec.bat and watched each time to see what happened, until I found the culprit, but at this point I let inspiration take over. A little voice in the back of my head told me that the EXPLOSIV.COM DOS screen saver was the most likely source of the problem, and so I restored config.sys and autoexec.bat back to their full and original state and simply commented out the load of EXPLOSIV (which goes in as a TSR) in autoexec.bat. That was it - that did it! With EXPLOSIV not loaded, Windows again ran for over an hour before I terminated the test.
So, I can only conclude that EXPLOSIV, which is set to run after 15 minutes of inactivity, was starting up even when Windows was running, and in the process, was conflicting with Windows in a sufficiently destructive way as to freeze the machine. So, a poorly behaved DOS screen saver was "taking out" Windows after 15 minutes of run time, every time.
This is the "fun" of DOS and Windows - when things go wrong, they often don't provide meaningful error messages or worse, they provide misleading error messages, or even worse, something apparently unrelated goes wrong, pointing the debugging effort into totally the wrong direction. The "fun"? You have to apply a LOT of creative and critical thinking to the issue and try to suss out the root cause. This is rarely easy and often takes quite a long time.
In this case, everything pointed to an incompatibility with the new RAM, and yet the incompatibility was with an old screen saver. That incompatibility had been there since I installed the screen saver a year ago or so. It is just that until recently, I had not run Windows long enough since the DOS screen saver was installed to encounter the problem. This only happened when I was running what I thought were stability tests for the new RAM. Sheesh!
Anyway, thank you ALL for your thoughtful comments and suggestions! MUCH appreciated!