I've also thought about doing a plate of aluminum across the back. The bottom layer has a few signal traces in it for the temp sensor, but otherwise is for the most part absolute ground plane - which means chips aren't belly-pad-sinked into it directly like on the S5, except on the bottommost node. This thing is designed for top cooling. I can change that layer around if necessary to give it a bit more heat flow into the rear face of the board without a lot of trouble, but then you have to make sure your heatsink is electrically isolated which tends to increase thermal resistance. That's a big reason most string boards are top-coolers - having 15 different voltage-potential planes all rubbing up against the same block of aluminum can get fairly risky.
If I retool for a different chip whose dimensions are any larger than the BM1384, I'll probably have to either go with fewer chips or give up on the CPU cooler. It was darn difficult to fit 8x 8x8mm ASICs in a 30x30mm space with room for routing. Any bigger would be impossible. But I could just build for a basic heatsink, maybe 80mm square with a case fan mounted, and make the chip field any size I wanted to fit underneath it. Of course I'd keep the same size and screw positions on future boards which could mount up to the same heatsink.
I see your point about a back plane cooling, if its not all a common ground plane, then:- "magic smoke"
Some plastic standoffs and a secondary "case fan" will be a safer base plate.