I ran this type of listing for a client recently, to liquidate her major "fixer upper" property in an EXTREMELY desirable part of Bellingham, WA, known as Fairhaven. The way we protected against the scenario you describe above was to make it widely known that NO offers would be reviewed until the 6th day after the listing went live. We ended up with 12 written offers (6 others backed out in the last hour) and we sold for all cash, no contingencies, 10-day close, for about 25% above list price. It was very much "fair market value" in the end.
A few points that were driven home during that experience: Your listing agent should have a policy from the get-go that they will not represent or assist any buyers whatsoever. Every buyer will need to get their own buyer's agent and compete on equal terms with everyone else. I had at least 4 or 5 buyers come straight to me and ask for "favors" to get them the house.
Also, in retrospect I would've run it for 7 full days and looked at offers on the 8th day. A little more time would've likely netted the seller a little more money.
Next, we made it 110% clear to everyone that we were definitely going to pick an offer, so put your best foot forward from the start. Dot every i and cross every t, bring pre-approval letter or proof of funds with your offer, and don't hold back. Show us your cards, because there will be no second chances. Another way to approach it would be to say "We're going to pick the top 3 and give them all one chance to revise." As long as you're up front.
Finally, to get this sort of frenzy going we priced it at a ridiculous low number so it gained lots and lots of attention. Don't come on at 3% under fair market value and expect an auction like we had. I've seen other sellers do that, and it will backfire on you.
Best of luck!!!