Hi Joe, welcome to permies.com; sorry to hear of your tree-woes.
I don't know anything whatsoever about this tree, never heard of it before, but letting your branch dry out would be problematic, best to get it into something asap. Water if nothing else.
I did find a post on gardenweb talking about propagation of this tree, which suggests it requires great care to keep moist/humid, and greatly benefits from bottom heat in well-draining but moist medium.
http://forums.gardenweb.com/discussions/1934214/ylang-ylang-trees-propogate-cuttings-or-buy#
You could consider stripping off the leaves to help keep transpiration down. You should have enough pieces to try quite a few different variations, as you shouldn't need a very long piece for each attempt. So, some variety in potting medium could be good to see what works best. For example, I only succeeded with elderberries when I used peat-moss on top of vermiculite.
Good luck!
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