My overall takeaway from trying to find DIY fishing in the Keys has been sort of similar to doing it around here; lack of access to productive water and crowding in the available spots make it challenging. Additionally, the enormous amount of water, only some of which is productive, make it hard to know where to put in effort. A guide who knows where the fish live and has a fast skiff to go between spots makes an enormous difference. Of course, I have never spent more than a few days there, and I've generally been with family, too, so my experience and knowledge are extremely limited. Someone who knows the area will probably have more and better suggestions.
That said, aforementioned Bahia Honda is known to be one place where you can get access to flats that have fish on them. If you go there, you'll notice along the surprisingly long drive from Marathon that there are a lot of people fishing from bridges. Obviously, that's a bait game, but it's probably the best odds of catching something DIY without a boat.
If you can find a place to rent a kayak for a few hours, you could probably have a good time exploring mangroves around navigation channels. There are lots of fish in those areas that can be caught on flies/artificials. If I have a chance to try the DIY thing down there again, I think I'll try that.
Finally, February, while it can be good fishing, is prime time for cold fronts, which push the fish out to the reefs and beyond and really screw up the nearshore fishing, sometimes for a few days. Guides won't even take you out when a front comes through; it really is that bad. The good news there is that the weather behind a front is what a PNW dweller would consider fantastic (low-mid 70s). Perfect for walking around and enjoying the relaxed vibes and bountiful seafood with the fam. It's a good place to be a tourist!
Have fun, and good luck!