What kind of sunscreen are you wearing? Admittedly, I have never been to Arizona and have no idea how well the same sunscreen that works for me here in Indiana would work there. It sounds like you'd rather cover your legs entirely, but perhaps a different sunscreen would suffice. I love Neutrogena Dry Block w/ Helioplex (I think that's what it's called). I use the SPF 50 and haven't had even the slightest burn during long rides. It rubs in very easily and is not at all greasy. You won't even notice you have it one. I like it a lot more than Coppertone Sport.

You might also try Shebeest Pedal Pushers. They're a padded knicker that hits midcalf. That plus some sunscreen would give you pretty good coverage.