According to ancestry.com, a man named Rex Gavitte married a woman named Alice Weiss in Philadelphia PA in 1926.
So Alice, it would appear, had already been Rex's wife for a few years before Rex took Bix home to Long Island for some rest in mid-June of 1931.
Of course I'm sure you'll be in contact with the Weiss family and ask them about that.
As for Bix reversing the last names of Alice's parents and making monetary claims about his supposed intended no man working as a waiter and supporting a large family could possibly have come up with to leave behind to his daughter -- well, to me that's pure Bix. Not surprising at all. Looks like Hoagy may have played along, too, by referring to her as Helen (which doesn't surprise me, either). I've always wondered, though; how did "Helen" know to give Bix's mouthpiece to Hoagy?
This is all very interesting indeed. My congratulations to Chris on his detective work and thanks to the Weiss family for being so forthcoming. Well done you, too, Albert.