I fish the same area out of an 18ft flats boat. To me this is a good compromise as it allows me to pole the icw banks as they are deeper and use a trolling motor. I also can cross larger wakes and the harbor more comfortably. All this while still being able to get into the grass on flood tides. Very rarely are we running expansive shallow flats here.
Plenty of older quality flats boats available in the price range with good power.
I feel like my Hewes lappy is a great all-around boat for the Charleston area, and you can find them in your budget pretty easily. It gets skinny enough for nearly all of my flood tide flats (very infrequently I may get out and wade), I am a little limited at times in skinny low tide creeks, but I almost exclusively fly fish and it has served me very well for the last 4 years or so. Plus, I can run across the harbor or fish the jetties no problem. I would feel comfortable cruising the outside for kings or tarpon, and setting up on the inlets to fish bait for big reds or tarpon is easy too.
If you exclusively fly fish and prioritize getting skinny over a little open-water capability, maybe look at a Mitzi or Salt Marsh/Ankona. You'll get beat up in the harbor or even when the breeze picks up in some of the rivers, but that's the tradeoff for super-easy poling and skinny creeks. I can run 40mph through slop in the Hewes, but I've got to put a little more work in when it's time to pole the boat around.
I would make the road trip down to Miami and pick up one of the two Maverick Mirages for sale in the first few pages of the boating and fishing products for sale, one is a 97 for 13.5k and the other a 92 for 11.5k, both super sweet boats and great deals for a boat that you can forever upgrade and get super value out of! I fish out of both of those model boats multiple times a week in super snotty conditions off the beach and super shallow conditions in the bay and they are the best! Jump on it quick!