It boils down to a few things for us. We design the PCBs to be a small form factor with a lot of board support. The case is usually the heatsink which supports the CPU and GPU with a spring on the reverse side of the board to keep it engaged. Plenty of mounting holes on the board. Internal cables are supported, etc, etc. Larger inductors, caps etc are glued to the PCB instead of just relying on the solder. That kind of thing. Upshot is that the casing can take a belting or a decent shakedown without an issue. These already fairly rugged units are then mounted (via quick release plates etc) to four shock mounts from these guys: Anti Vibration Mounts, shock mounts, vibration isolation products, isolators, anti shock, aircraft illuminated control panels This softens the ride and soothes out the vibration a little. Surprisingly, maybe, they're not soft - they don't move a lot in response to being pushed by hand.
Given that you already have a stock motherboard, and you've already mounted it to a separate plate, it's going to make the mounting more important. I like the idea of just hanging it free from a couple of bungees - two each corner would have it just floating. If you wanted something a little more secure, though, I'd think of maybe making (or buying, if you can find them) some 90 duro silicone rubber standoffs about 10mm x Ø6mm with embedded 3mm studs for the motherboard. If you're feeling lazy, might even be worth just buying the canoe clip style nylon standoffs instead of using metal ones - it should give you enough slack to dampen some of the buzz.
In all honesty the nylon standoff are probably about as far as I'd go myself. Motherboards are cheap, if it dies just get another