Welcome to desirable remote places in Latin America.
Do I know a guy? Ha, I know you will have to change your dates. Or vibe code a Portillo lodging refresh. Or...I often call or write managers/front desk employees and ask to keep me in mind. Often rooms are kept offline for VIPs or hotel discretion.
Or if you can get a date at Ski Arpa Snowcat (Los Andes base), one could stay in Los Andes and commute up to Portillo. They sell lift tickets that include lunch
One can recreate Miami in Rio at a fraction of the price: (Copacabana or Ipanema beach hotel with view ($100-200), beach chairs ($5/day), and drinks/food (3 beers or Caipirinhas for $10), Acai ($3)), Lots of Steak. Latin America's large cities can be cheap. One day in Miami Beach = Three+ in Rio. However, if you want to go to Patagonia, Machu Picchu, the Galapagos, Iguazú Falls, or skiing (Las Lenas, Portillo, Valle Nevado), you have to pay Western or Gringo Prices - the equivalent of any desirable North American location with corresponding availability.