I just realized that the XHA1 captures HD audio at 16it.

What if I picked up a 4 channel field recorder like the Roland R-4 Pro? records at 24bit and has SMTPE time code. Product link:Edirol / Roland | R-4 Pro 4 Channel Portable Field | R-4PRO

Take a feed from the Uke's D.I. with a splitter.
Take a feed from the Sound board.
And use a stereo condenser like the Rode NT4 or similar to capture ambiance.

Feed all those into the Roland. Then use the on camera mic as reference. That might cut out the phasing and drifting problems when I go to sync it.