Move.
Move.
If you have a few cracked tiles, just replace them using the left overs from the original work or hunt down the tile and buy more.
If that's not appealing, tear up the original tile and near the cabinets, remove the kick plates and remove enough tile to get under the cabinets.
OR
Use one of these:
On Sat, 24 Jul 2021 12:43:08 -0700, Bob F posted for all of us to digest...
That's the correct answer, if you want it to last.
And get another contractor. Why would a competent contractor balk at having to remove the cabinets to do it right? They just screw to the walls. Sure, it's more work, but they get paid for it, they can put it in the quote.
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