Don't be a wimp Craig! Be a man! Let the bugs feast on you. You are providing valuable blood for the Everglades ecosystem :) (they actually say this on the Anhinga trail).
Even during the Christmas time, I saw lots of available spaces for Flamingo, so you might be ok. Here is what I did. I booked my spaces for 3 nights in Flamingo (the only campground that has reservation). Upon arrival to the park, I transferred two of the nights to the Long Pine key campground (they let you do that without any probs). I spent the final night in Flamingo. you could do that too.
For bugs, after what I experienced in Biscayne, Flamingo seems to be an easy walk in the park!