Ive done a few of those tight real estate gigs and the Sony FE 16-35mm F4 G PZ is probably your safest bet for gimbal work. Since it is an internal zoom, the center of gravity doesnt shift, which is a lifesaver when youre moving fast. It sits right around your $1200 budget and the autofocus is super reliable on the FX3. Heres a couple tips for those tiny rooms:

• keep the camera height at mid-chest level to minimize perspective distortion
• watch your corners at 16mm because things can get stretchy if the camera isnt level The f4 aperture is usually plenty for real estate since you want most of the room in focus anyway. If you really need the speed, the Sony FE 20mm F1.8 G is solid but it might not be wide enough for tiny bathrooms. Good luck with the LA shoot next week.

Building on the earlier suggestion, I've been super satisfied with the Sony FE 20mm f/1.8 G for those tight spots. > the rooms are tiny I had a job last month in a cramped condo where my 24mm just wouldnt cut it. I was worried 20mm wouldn't be enough, but it hits a sweet spot. The main reason I love it is the lack of distortion. Real estate clients are picky about vertical lines staying straight, and this lens keeps everything looking natural. It's a beast. Plus, its super light on the FX3. I can fly it on my gimbal for hours. Since it's a prime, the balance never shifts. If you really need wider, the Sony FE 14mm f/1.8 GM is incredible too, tho it might push your budget. Honestly, no complaints with the 20mm... it just works.

Big if true