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The answer to this problem is a "chickenwire cage". Hold the big lump together but let the sparklers fly. :)
A shallow pool of water you could wade into? Wait, doesn't the Thames have some sandbanks?
My simple solution would be ducttape or another bit of the masking paper (can also be the rest of the used one if bigger bits are left in one piece). Put it on the isolated cut pieces and pull off. Repeat until clean.
I have cut circular O shaped adapter pieces from plywood sometimes if the bottom and top of a glass differ too much in diameter. This way the overall slope is at least halfed.