RESOLVED!
After some testing, I noticed that the benchmark discrepencies no longer occured when HIMEM was loaded if I disabled the L1 cache on the CPU. However, I beleive that the issue is due to the benchmark software being run on a non-cached region of memory. Why do I beleive this?
Normally you set the 1st 64 KB of each 1 MB of RAM as non-cacheable. I don't recall the exact reason for this, but did notice that if it is not set as non-cacheable then many 386 boards will have problems loading (or within) Windows 3.11 if using a 386 CPU with L1 cache enabled.
I seem to recall not needing to set the 1st 64 KB of each 1 MB of RAM as non-cacheable when in DOS though.
Most 386 boards which support the Cyrix DLC CPU automatically set the 1st 64 KB of each 1 MB of RAM as non-cacheable. The issue arrises if you are using a benchmark program which happens to use this region of memory. Whether the benchmark program resides in this region while being run varies by motherboard and whatever else is loaded, e.g. HIMEM.
There is a cyrix.exe command to disable setting the 1st 64 KB of each 1 MB as non-cacheable. It is cyrix.exe -m and when using this command I no longer notice the benchmark discrepencies. There are other non-cacheable regions which normally get set by the BIOS; I think it is 640K - 1 MB. This can be set to cacheable with cyrix.exe -i1 -i2 -i3 -i4, however keep in mind that Windows probably wants these left as non-cacheable.
For consistency between motherboards, I think I will need to set the noted regions as cacheable. I will also continue to load HIMEM.
Some motherboards might have floppy write issues if these regions are set as cacheable. I forget which motherboard had that issue.
Plan your life wisely, you'll be dead before you know it.