Is your power supply stable ? especially the +5v line.

I'm pretty confident the power supply is stable.

I'm not sure any power fluctuations would account for the alternating memory errors during testing cycles. When I test the power at the chips they all show the same voltage around 4.87V, including the ones that would be in error.

just an FYI, While 4.87v is within the ripple margin, it can be a cause for intermittent troubles.
Have the PSU and/or mainboard ever had their electrolytic capacitors replaced, that you know of?

I've had to replace some of the ceramic caps that popped or were running hot on the board. They were at the head of the memory chips. I did not change them all as the others weren't running hot or showed any signs of concern. I guess I could change all of these.

For the power supply, I visually inspected it before power on and checked the outputs and all seemed fine so I didn't re-cap anything in the power supply.

I'm afraid that maybe focussing on the memory system is too narrow. I agree with your conclusion that the memory chips are unlikely culprits if they work reliably in a different system, and the problem is not specific to the address range of a single bank. On the other hand, this means that anything connected to the system bus (ROM, ISA slots, on-board components) might interfere with the data during memory access.

The intermittent problem you observe is a typical symptom of a broken or bad connection (but there may be other causes, too). Often, it is stress induced by thermal expansion of PCBs and/or chips that makes the difference between a working and a non-working system. Another plausible cause is probing with thick wires in classic DIP sockets. It might bend the springs far enough that they don't have enough pressure to correctly contact an inserted IC. Another possible cause is soldering such sockets with an IC inserted. If you heat up the socket while an IC is inserted, the clamping force might deform the socket when the plastic gets soft due to heat, resulting in a too low clamping force after cooling down. If you soldered all sockets in the same way (for example with chips inserted), you might have damaged a lot of your sockets, causing issues with different random memory chips.

Oh definitely I didn't solder in the new sockets with the chips in them. And also didn't push my probe into the socket when checking the sockets.

I don't think thermals are playing a role in this. As I mentioned sometimes it will happen sometimes soon after first power on after 12+ hours of sitting. Sometimes the machine for more than 9 hours with no issues. And when the board did mess up, I even tried to freeze the board and it had no effect.

Also I'm not sure the thermals would apply when you consider the the memory test loops is like 1-2 minutes apart. So I don't see how thermals in that short of a period could affect 1 chip on cycle then 6 chips then next, then 3 chips the next, then no faults the next, etc... I've also used a thermal probe to check the temperatures of items on the board. There's no longer any areas that are warmer than expected. So no longer an warmer caps and no warmer than others memory chips.

I'm still worried it might some of those LS chips that are "aging" or may be damaged by past problems on the board since 11 of 16 memory chips where dead as well as a few popped ceramic caps. The other piece you mention is the possible bus issues. Floppy controller, HDD controller, video, serial, parallel, and RTC are all on board. But those issues might not be evident without a scope. I've run the system with and without Floppy and/or XTIDE and the same issues remain present.