OK, last update.
I've spent the last two weeks running hardware checks, and troubleshooting, and moving RAM sticks around. I've not only figured out what did it, but managed to reproduce the issues as well as fix them:
The RAM is in matched sets. Each pair of 8Gb sticks has sequential serial numbers, but the two pairs are quite a bit different. The MSI MB has four DIMM slots. Slots 1 and 3 are Memory Channel "B" and slots 2 and 4 are Memory Channel "A".
If you mix the pairs of RAM on the Channels (i.e. one stick from each pair on the same Channel) all hell breaks loose. As long as you keep the pairs of RAM together, and use channel A before B if only running one pair, everything is stable.
On intial assembly I just opened the RAM sticks and installed them left to right across the DIMM slots, which caused the problems because the channels alternate. The instructions did mention using slots 2 and 4 if you were only running two sticks, but I had no idea the RAM sticks that came together were "paired" together that hard.
I'm still pretty glad I went this route, as It's a pretty solid computer now, and having a Windows install without all the OEM bloatware on it is really nice. With 32gb of RAM (working) and the M.2 SSD the computer is blazing fast for anything I will use it for, and reasonably future proof.
Thanks to everyone that helped me out with the parts picking and troubleshooting.