This is the only solution I think might work. Tax vacation rentals and empty properties at a higher rate...while allowing tax discounts for keeping rent low.
Genuine question: Why is enforcement so difficult? Let everyone declare their primary residence and give property tax credits based on the number of occupants (with pass-throughs for rental properties, etc). Everyone has an incentive to declare a primary residence and it shouldn’t be too difficult to find people declaring multiple.
You could cap the number of occupancy credits per sqft to keep things reasonable.
It would also help with things like state taxes based on primary residence.
Unfortunately, I think the crash will come first