1. What is your target market? If like many adventure travelers they are not yet retired, how responsive can they be to your just-in-time, go-next-week offerings?
2. If you want your customers to "ultimately be responsible for the cost of their own flights," and they don't even find out about next Thursday's tour until today, how are you going to persuade them to pay close-in fares? It sounds like you want some secret work-around that lets you obtain advance-purchase air tickets at near-day-of-departure rates; those don't exist on a consistent basis.
2. What is your value proposition? What can you do for me that I cannot do myself with 30 minutes' surfing? You are not proposing to introduce people to Myanmar or Siberia; you want to send them to Colorado or Montana. Chances are your market knows those places already.
Look at the cruise industry. There are basically two tiers to it: long-lead purchases, where the itinerary is marketed, sold, and paid for by the customer 6 to 18 months in advance... and the short-lead, distressed-inventory, deep discount market, where the ship leaves in a week from Rotterdam or Papeete and empty cabins can be yours for 70% off if you're free and can find a way to get to the embarkation point on your own dime.
You will note that the distressed-inventory, close-in market rarely if ever includes free / discounted airfare.
The market has organized these models rationally. You want a difficult-to-execute hybrid of those two models: all the complexity and logistic effort of advance-planned trips, offered on a hey-let's-go-now basis, at high prices, to people who probably have jobs and busy schedules. I am not sure how you intend to thread the needle and pull this off.