This:
http://www.youtube.com/watch?v=zsRsK2tm7Gs
uses a sort of combination H and fan bracing system, though so massive that I'm amazed it wasn't completely silent! But it might give you some ideas. It's a copy of the Gretsch Camp Uke, which wasn't famed for its sound quality. Note the bridge placement, which is far too near the tail but was presumably put there to make it shorter and more transportable.
Thinking about it, if you have a bridge patch I can't see why you'd need the H cross-piece for strength, though it might do something to shape the sound (quite what is guesswork). I'm a fan of light as possible, but this is based on intuition not research.
The original Lyon and Healey Camp uke is interesting - no soundhole but a resonator back. See here:
http://antebelluminstruments.blogspot.c ... ulele.html which linksto four more examples.
This thread gives you some dimensions and bracing (either one transverse brace or no braces at all):
http://www.ukuleleunderground.com/forum ... l-Ukuleles
Good luck with your project.