VAT is such a PITA (I'm originally European, so I know a thing or two about it). Tons of additional paperwork, plenty of room for fraud and cheating (like https://en.wikipedia.org/wiki/Missing_trader_fraud ).
Just be honest about it, increase existing property taxes, which people already pay anyway and are naturally progressive and avoid creating complications.
Also, I would start with lower amounts, and see what actually happens.
And ... Why wouldn't every capable homeless person from all over US move to California if they would be paid to do it (and I can't imagine more forgiving weather for homelessness, anyway)?