At the moment I'm still using a stack of cheap and nasty 8mm plywood for Crown Boards. This stuff was employed to separate layers of tins of paint etc stacked on pallets - so was always intended to be 'one-use only' and disposable. You're right about plywood warping - it's real pain - which is why I'm gradually moving over to using Foamex (a 'dead-flat' man-made material) instead.
But used as it is on the Clemens and similar boxes, this plywood hasn't warped. Two reasons - one is the weight of the box (feeder shell) and roof holding it down - that's about 4-5 lbs. The second reason is that the girls have well-and-truly glued the Crown Board in place with propolis, so even when I lift the box weight off, it stays well stuck down. All I do is crack the board off to work with the bees, and replace it afterwards without cleaning-off the propolis.
Ok - swapping brood combs over. I shake-off (*) the bees on both the combs being swapped, to prevent any fighting. The old brood comb goes back (usually) to the hive it came from, and a new comb - containing at least a good proportion of open brood (larvae) - is donated to the Clemens hive. It's the pheromones being given off from the open brood which prevents the development of laying workers.
Now because open brood is being given to a queenless hive, there's always the risk of unwanted queen cells being started. So I find the best time to donate the new brood frame is a couple of days after they've started drawing the q/cells that you want them to draw. Then, as queen cells have already been started, they're unlikely to start any more - and by the time you remove the drawn q/cells, larvae in that new brood frame will have passed their sell-by date. It's still a good idea to check for rogue q/cells every 4 days or so, but using this timing I haven't yet seen any ... however, there's always a first time !
(*) To save bees ending-up on the floor, I've taken to using a 5-frame nuc box (no top or bottom, just the box) when shaking-off bees. Place the nuc box on the hive, and then shake the bees off the comb and into that empty box.
If you want to shake off bees into a working nuc box, then first pull the frame and place it onto a frame holder. Put the empty nuc box over the working nuc box and then shake the bees off as before.