Date: 2019-06-10 09:01
Well, from what I see about the Phoenix climate, it looks like an average of around 8 inches of precipitation a year. I live in a climate with 11 inches of precipitation per year. Not exactly close, but closer than some.
What most of us used to do here (I don't routinely play wood instruments anymore - unrelated reasons) is the old pill-bottle method. We'd take a sponge, cut it to the right width (depending on the size of the pill bottle this would be 1 1/2 inches or so) soak it, then (folding it in a bit of a U or V) we'd place the sponge in one of those small prescription pill bottles, and cut the sponge off just proud of the pill bottle top, pour out any extra water which had pooled, then placed the bottled sponge (no cap) in our case.
This worked great in our climate. Depending on the season, the sponge would need to be re-saturated (or rotated with a clean sponge) every three to seven days.
Some folks frown on this method, or use variants of this method...so use it at your own risk. It's the only thing I ever found that worked consistently up here for me (we're at 7200+ feet in elevation and deal with pretty strong sun radiation outside in the summer, and pretty terrible dry cold in the winter...so, while I've never had an instrument crack, myself. I've seen plenty of them crack.)
Best of luck in your search for a solution!