Well, this isn't an everyday challenge you've set us, but here are some thoughts:

In a more conventional cat, I'd say to put a mast in each hull, but in this case,there doesn't seem to be any ability to resist rotation of the hull relative to the deck, so that's out.

So with a central mast, the rule of thumb would be that an unstayed mast should have 10% bury (10% of its length) within its support. I would suggest that you set up a short tube into which the mast can be dropped, and then add four wire or Dyneema stays from the top of this tube to  the corners of the deck platform on which it is mounted. This platform will need to be stiff enough that it will not twist under sailing loads.