This makes sense -- I think your best bet is going to be an open-air rig. Find a milk crate, put a pillow in the bottom. Sit the mobo on the pillow and suspend the cards above it using a wood ruler or something to hang them on. You'll need PCI-E riser cables which can be a hassle to find.
If you somehow find a way to get them all working in a case I'll be amazed. Rule of thumb from what I was researching is that 75+ is bad, and so is having the fans run at 100 percent. Fans break faster than anything else on GPUs.