What's the difference with if they are hoarded or they are removed from play? You can still hand them out on rebuys, if you have enough total chips.
If you invoke the two-chip max rule and the double board winner(s) already have two chips, just leave it in the pot like a kill chip for the next player without 2 chips to pull. Maybe award it only if the double board is a scoop, otherwise it comes out of play.
If you give it out to one player in a split pot game, guess I'd give it to second/bottom board, because that board doesn't exist without the chip, but that's totally arbitrary.
If I play a chip before the deal on a double board game, do we get a triple board?