I spoke too soon. I could get the other RAM I got this week to fail under intense conditions, so I figured it had to be the lack of the proper heatsinks, and the interaction with the Mac. After some experimentation with Macs Fan Control, I discovered that I could get the Wintec RAM to work. As mentioned, it just couldn't stand the heat. It turns out the problem is that it doesn't have a heat temp diode anywhere in them. So, there is no way for the Mac Pro to know what temp they are, and thus no way to adjust cooling for the RAM.
As seen by the Macs Fan Control software, there are two memory slots where the Mac Pro measures memory temperature. If you stick the Wintec in there, the Mac Pro sees no temp to measure, so it just defaults to baseline 500 rpm. (I had read elsewhere that when the RAM temp couldn't be measured, the Mac would default to full fan speed. However, what actually happens is the exact opposite, and the Mac defaults to minimum fan speed.) In this scenario the Wintec RAM overheats and fails. Also, if you put OEM Apple RAM with the giant heatsinks in there, the Mac Pro sees it but measures a relatively cool RAM temp, again keeping the fan at baseline 500 rpm. Thus again in this setup, the Wintec RAM overheats and fails.
However, it turns out the RAM I got this week included Kingston server RAM that just had standard heat spreaders like the Wintec, but which also includes the temp diode. It also runs just as hot (if not hotter) than the Wintec RAM. So I stuck the Kingston RAM in those DIMM slots with temperature measurement and suddenly the Mac Pro could see the RAM running really hot, and would then ramp up the fans to keep them from going over 80C. In this scenario, I could add the Wintec RAM and it would work, because the cooling of the Kingston RAM also cooled the Wintec RAM of course.
Unfortunately, while it works, I don't like this setup because the Mac Pro becomes periodically noisy due to the fans. Plus, when the Wintec RAM is installed, it cause problems with manual warm restarts when the RAM is hot so it’s clear the Wintec RAM is still problematic. I am currently using the Kingston server RAM with my OEM RAM. The Kingston RAM does cause the the fans to kick in a bit but it’s not as bad when used in combination with the OEM RAM with the big heat sinks.
I never thought dealing with RAM would be so complicated, but I guess that's what you get when dealing with server parts.