This may not apply to your case. But it was my experience that when I split the queen and 40% of the bees, and both colonies remained in my little apiary, I had driftback to the original hive. The old Q's colony got small and slow to build. It became 20/80 instead of 40/60. When the new Q started laying in the big colony, it wanted to swarm again. So I took the next split to a friend's house, and all the bees stayed. So then...I had 3 colonies from the first. :)
Re: using your TBH, at one point I made some frames, to use comb from a cutout (in pic). The sides have one pinhole, to pin it with nail or wire. The wood here is wider than is really needed for stability. Hope this helps.