One page website, effectively. Text input box.
Question: Can I buy this with bitcoins? User inputs the answer in the text box, hits a button/enter.
The thing they want to buy with BTC (and their approximate geolocation via IP to help narrow impractical/impossible shipping feats) is broadcast to a ticket system and a live chat channel with agents.
Agents review the tickets/see incoming requests, then hunt down the stuff across all the bitcoin sites they know of, reply, and the page reveals the answer(s) to the user.
The page can be set to request an email address for a notification after a preset time without an answer other than "no" (which should be blocked anyway, as the goal is to prove that there's nothing you can't buy with BTC).
If the agents were able to cover all 24 hours and be competent searchers, then the notification wouldn't be required.
Not sure how to monetize it other than the searchers being shown which agent(s) answered them in which timestamped order and their BTC address for a possible finder's fee donation. The site owner would either be competing with the other agents or require a nominal fee to be one of the agents.
The only people who will know what potentially embarrassing stuff people want to buy will be the agents, who will be firewalled from their actual identities regardless of whether they answer before the 'request notification' time limit is hit or not.
Subject to revision.
At this point, think of it as a stripped-down, private Rugatu.
*I would want to be one of the agents, as I have over USD $7K worth of stuff for sale.