Late August, early Sept, it is mainly.....hurricane season. And even if the big blow doesn't hit, it is still very hot, humid and wet. And it's the peak season for unpleasant insects. You will get shorebird migration in August, otherwise better later.
Summer is also the quietest time of the year generally for birds - only 28 summer visitor species, compared to over 120 winter visitors. So, if you have any choice in the matter, wait until October.
Specific sites - the Everglades is generally a disappointment, for various reasons, partly size/inaccessibility, partly years of drought, partly being generally less birdy than assumed - since a lot of it is uniform, featureless plain and very little is actually the steamy swamp of southern Gothic that the movies would have you believe. It's not terrible, just not that special. The Dry Tortugas - only visited in the spring, opinions differ as to why. Some say there might be birds there in the autumn, others say they've gone and there's nothing there. (And Ding Darling's nothing special either.)
On the upside, autumn gets you great birding up and down the coasts and on central wetlands. Try Fort de Soto, Merritt Island, the central lake chain (including Joe Overstreet, Three Lakes, Lake Kissimmee State Park, Lake Tohopekaliga and Lake Jesup), Split Oak, Circle-b Bar Preserve, Colt Creek, Wekiva Springs and numerous similar locations.