Additional dry rock is great, but does nothing for the uglies. The only thing that entirely stops the uglies is starting with rock that already has non-pest algae established. Live rock is a blank canvas, and pest algae thrives on new places it can run wild, without competition. The non-pest algae is all the slower-growing stuff that needs time and nutrients to get established.
I assume you're going to get rid of the bubble algae rock after everything is transferred, right? In that case, I'd suggest you move everything over to the new tank (slowly! Very slowly!), then, when you have just the rock in the old tank, try Vibrant. Then it can't hurt anything if it fails or goes catastrophic.