My friend does some contract work, and knows that when the job will be "difficult", he just over bids by the amount he would not be able to refuse the job. These guys know that with the restrictions that they put in place, they will have to pay more to get it done right,,,, according to their rules. Your company was invited to bid, so there must have been prior recommendations that your company was good enough for the job. Bid the heck out of it item by item, and deal with the nitpicking that they are willing to pay for.