If they have tons of liquidity but all these red flags, you need to simply adjust your deposit for the risk you are taking. Assuming your laws do not limit the deposit and you have consulted an attorney, just CYA with an appropriate deposit and an iron-clad lease, full credit check, detailed application form filled out and checked.
One your applicant has “skin in the game”, he will perform or pay the price. (a lesson lenders disregarded a few years ago)