If you use a modified Warre hive that has movable frames then you should be able to do OTS in a Warre system. Almost all states in the USA require the use movable frames anyways. With a Warre you could do it with standard Warre boxes. A Langstroth nuc won't be compatible and you don't need to make a smaller box than the standard 300mm x 300mm.
If you wanted to follow the MDA method You'll need five bottom boards and about 12 Warre boxes with frames, 5 quilts, 5 feeders, and five tops.
I am skeptical that a brood break alone will adequately control mites. But an OAV treatment during the brood break would be highly effective.
Note there is the OTS queen rearing method, and then there is the MDA system that uses OTS twice in a season, first to create brood bombs and then again to create brood breaks. The two should not be confused.
Warre equipment is ridiculously expensive, hopefully you have the skills to make your own.