what size tank? how much live rock? How much are you willing to spend and/or work are you willing to put into it?
Like geoplane suggests, have you tried remedies, such as rabbitfish? They say emerald crabs eat them but to me that's a joke. I have an orange spot rabbit and a fox face with no visible bubble algae. It grows inside the overflows and in the algae scraper along with other crevices the fish cant reach. They do a great job keeping it in check and it will become a problem again if I remove the fish.
There is also some other crap in a bottle, Vibrant I think it is, people have had succes using that, I didn't.
As for restarting, remove rock give it acid then bleach bath. Clean and disinfect the tank and all equipment that will touch water. Or start over with new dry base rock.
Here's the catch, any corals that are kept in holding tank and are attached to a substrate or have a dead skeleton such as some lps. When place in the new tank have a great potential to introduce the algae right into the new system.
I have started over a few times over the years. AEFW, Vermetid snails, bubble algae, bryopsis , monti nudi's or just burned out with maintaining full blown sps tank.
My suggestion is to try to remedy the bubble with some manual removal and rabbit fish. If definitely starting over (i get it) start with clean dry rock and clean scaping of coralline to seed the new rock. Cycle the hell out of it as it will take some time to become stable and mature enough to support SPS. Then when you do restock use fresh cuts with no substrate or plugs. Can scrub lps skeletons and or substrate with peroxide being careful not to kill the polyp to remove potential bad algae. Chances are with doing above you may introduce bubble algae into new tank and be back where you left off