Good luck. I found myself in a similar situation with pretty good estimates, but unable to bid low. I'd be bidding double or triple the competition. One time, I was bidding at triple, and the previous dev had failed totally. They went with another dev who bid nearly the same price. He failed, too. By that time, I was like, I'm not even going to bother - they don't want to pay what it takes, and buy failure over and over.