That's a really interesting question and dilemma!
And might I add, so cool that you love playing Santa so much that you even grew out a beard to do it! Fabulous!
I would assume since you've spoken to major companies, and salons, that they have considered whether bleach (as in the hair type) would work to turn gray hair white... bleach will remove color from your hair, but gray hair doesn't actually have color, per se. I'm assuming they've told you that bleach won't work?
The only other suggestion I'd have, would be to use something less permanent, like the color sprays. Perhaps you could use a little in the beard and hair to whiten it up a bit? I wouldn't suggest trying to completely whiten your beard and hair with it, because it would look odd. But if you just lightly sprayed it, to give it a dusting of white, so to speak, it might give a more realistic appearance of white hair. Worth a try, since it's not expensive, and completely washable, which is the other plus. You could shower after a job, and not have to deal with any irritation. Not sure how well it would hold up, though, and not rub off on your's or other's clothes. I'd still give it a try, if you haven't. (Not sure exactly what kind of 'theatrical make-up you've already tried.)
Oh, I just thought of another suggestion... you may have already done this, since you mention using theatrical makeup... but you might try consulting with a local university's theater department. See what they do to whiten hair/beards... just another avenue to check...
In any case, have a wonderful time playing Santa. It's so cool.
And I did find InMy30'sAlready's response to be quite humorous. :)