The town I am located in had this same issue and saw it happening to an extreme elsewhere in the country. So they implemented restrictions on how many Vrbo and Airbnb's a person can have active at once.
It unfortunately didn't take affect retroactively, but it was immediate. Which was really funny to see as some recent purchases and renovations were suddenly put on the market again after the city pulled the rug from under them.
As I understand it, you can purchase whatever you want, but to Vrbo, Airbnb, etc, you must register the property with the city as a non-permanent residence, of which, there is a limit of one per organization or individual within city limits.
Totally cheesable, as one could be in a spouse's, or dog's name or some other rich people crap. And again, not retroactive, which sucks as housing is still a nightmare here.
So my advice. Get a petition going with a similar solution put together. Get into some city council meetings. Get vocal. Make some cool posters.
This solution won't target tourists, and may take longer. But in my mind, it will target the real problem.
Yup!