Instead of trying to modify a tub to what you want, I think it would be easier to start from scratch.
A sheet of plastic, some wood, and a piece of plexiglass could be used to build a drawer style cage.
You could also make a custom glass tank that would fit inside the opening.
Both methods I listed would have a raised bottom panel that the UTH could be attached to. it will mean that the cord and probe will have to have some slack in them, but they should't rub.
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