Strollers: go to craigslist down here, and they have lots of strollers for sale on the cheap. Or, wait till you get here, go to Babies r us, and get their Zobo stroller. It's usually $99 or $79, depending on if it's on sale, and it's a great umbrella stroller. Good shade, easy one hand fold, very slim and stands up when folded. Did I mention it also comes in SUPER bright and different colors (neon green, bright pink, purple, teal, and red). AND it has a cupholder?
Shade and sunscreen are both very important down here. But that's what I would do, and besides, you could always use another stroller! Maybe it could become your "travel one", and you could leave the big one at home when you decide to do major travel. And no matter what you do get one with good shade. I see lots of folks here with miserable strollers with no shade, and the kid is practically burning. (Maclraens are pretty bad, for all that they cost. Graco is another Florida no-go). So test them out, but I do like the Zobo for the $$ and the shade.
Just my .02