Two auctions is a great idea Mizzoula, that solves the problem. I'm betting the dollar auction takes off and the second nights auction will be a sleeper. The second would be more of a showcase for what you're willing to part with. And then you would see everyone switching over to the one dollar auctions, but it does diffuse the debate.
I think if the bids went up like an actual auction that would work. While the first bid is a dollar, can't you raise it to $10, then if someone wants it for $20 that's the current bid. This $1 at a time thing takes to much time. If I'm willing to pay $50 for a domain, let me bid $50, and if someone wants to top my bid, then they set the next level, and if I want to set a higher level then that would be the new mark. Why does the policy have to mirror e-bay, this $1 increment only smells like trouble for the seller. I predict you'll see tons of offers 2 seconds before the auction ends, I wonder who's building a sniper program at this very moment. If I want the name and am willing to pay for it, I risk loosing the auction because I'm limited to what I can bid, the auction becomes a button race.
Now if there is additional time put on the clock for last 2 second bids, then that would work. Lets say you bid 2 seconds before the close, then the auction is extended for another 10 seconds. This would kill the sniper and allow fair competition, maybe the $1 can work.