That's funny. Did you buy the same toilet brush or is that some clever photo shopping?
I had a four year hiatus due to a catastrophic tank failure. I surrendered ALL of my livestock as refugees to my LFS. They were great to take them in.
The fine folks at TBS and I had great email exchanges where I described my tank, goals, and dreams with them. They absolutely nailed it in my order. I totally suggest you start a dialog with them. You cannot go to their storage facility and hand pick rocks. It is not a retail facility. Probably for insurance stuff???
For your situation, I might order a TBS "Treasure Chest" to start a 10 or 15 gallon half way house. I like this package for this purpose:
https://tbsaltwater.com/shop/pico-package/
Temporarily supplement with some ceramic media if you need more space for bacteria.
Scrub and transfer corals and what other livestock you can into the halfway house and then totally decon and clean your display. Slowly move rocks, corals and livestock back into the display, and plan the trip to Tampa for 20 to 30 pounds of premium live rock. Don't add sand until you have had a couple month to hunt and remove undesirable hitch hikers.
I know you are concerned about seeding the bad algae in the new tank, but I believe the reality is that real ocean live rock does not have available real estate for nuisance algae to take hold. See how it grows on the cord of my wave maker, but no where else?
I really wish you the best of luck. Go slow. Let me know if I can help...