Then single family homes owned by LLCs should be taxed out the ass. I know it's a cat and mouse game, but if a corporation is the owner of a home that should be a dead give away that it should be taxed at a higher rate than for one owned by an individual.

Indeed— like a lot of these things, it would punish upper-middle class families who inherit a cottage, but not affect anyone with >5 residences since at scale the work needed to evade becomes worthwhile.

There's already multiple rules for "primary residency", you could structure a progressive property tax off of that.