Not sure what your budget is, but tarps are not really a long term solution (especially in hurricane territory). Unless the tarps are taught, they will catch wind, rub, and eventually shred. A bad storm could rip them right off and leave your chickens unsheltered. I'd recommend tightening every loose area (zip ties, bungee cords, whatever it takes) to get the most life out of them before devising a longer term plan. The coop, in particular, should be hard sided so that they have somewhere safe and secure to go if the tarps fail.
Only other concern is the security of the run. Florida is full of predators and it looks like you are in a wooded area which will attract them. I can already see gaps on the lower edge which will make it easy for something to dig or squeeze under. At a minimum, consider an above ground hardware cloth skirt or surround the perimeter with cinder blocks. Did you run hardware cloth over the hog panels on the sides too? Raccoons and other predators are known to lure chickens to large gaps and then rip their heads off through even the most secure fences.
Make sure you paint that plywood too. Plywood will usually withstand some moisture exposure, but it may swell or delaminate if you leave it exposed long term.