First there is no dust, you have them use a wet saw, having a wet/dry vac remove a few quarts of water.
the existing hole can be used as a junction and recessed into the floor never to be seen, with a new tile in place.
the cutting is about $150, guess two hours labor for elec. 200.
Then tile work $100
not cheap but doable,
I added one myself not all that hard to do.
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