Both the Ivey House and the Everglades City Motel are a combined operation now... With Glades Haven still down, the few places available in Everglades City and Chokoloskee will be at their highest occupancy.
One alternative, with lots of rooms (and a pretty nice place...) is Port of the Islands, about seven miles west of the turn-off for Everglades City... You can either use their ramp (and do that three mile long idle speed zone) down to Fakahatchee then outside - or simply hook up your rig and trailer back to Choko to be able to launch and run south...
Good luck - let us know where you finally stay and provide a review..... There will be lots of folks reading it... When May first rolls around prices should drop for the summer and there should be lots of places open (excepting weekends until around June...).
Hope this helps... I'm working over there next week and I couldn't find anything cheap enough... since I'm only there to work.