We ended up working around the problem by calling the resize event every time the button link to that page is clicked. (we have all the "pages" in one index.html document) Now the map loads partially at first, but is resized quickly afterwards. It sort of works!
But there's still some wacky layout/DIV/design bug in there, I think. Hoping this won't cause more problems once we start adding location markers and other things depending on the map rendering correctly.
We are also experiencing very stop-and-go scrolling. I'm not sure if this is because of jQuery Mobile + Ice Cream Sandwich or what (that's how I'm testing it), but is anyone else having less-than-smooth scrolling in their phone apps?
-Ben