I think I've seen a someone build a BP rack with individually wired heat tape, all plugged into a power strip, then a thermostat. The goal was to allow them to save power and just unplug not-in-use tubs, but it sounds a bit like what you're thinking of here.
I'd just make sure to use a high quality power strip & thoroughly test that the temps fall where you expect off a thermostat. Don't see much reason it wouldn't, but ones plugged in further down the strip have the highest chance of losing electricity from the further travel distance.
Set up that way, it should all you to remove each tub/wiring at will for moving or any other reason.
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