If you have a rental contract that requires payment in dollars, use your passport and the contract for the rental to explain your need to purchase dollars. As of Monday, you might need to explain your dealings to an AFIP agent. So what? You have a legitimate reason to purchase dollars.
In any case, you are permitted to buy up to U$S5000 per calendar month as a non-resident in notes, checks or travellers' cheques without the BCRA's approval from any entity approved by the BCRA to deal in currency.
Has anyone had trouble purchases dollars for rentals paid in dollars since the changes, showing your legitimate reason for doing so?