| ...rhymes with misery ... and the answer is simple, give them your best-effort bid and give them comparison numbers from your competition. Then tell them that if they don't believe you, you will be happy to arrange a contact with the next lowest bidder.
This path takes a certain amount of brass, in your lower extremeties, but it usually pays off. If they are truely that difficult, then you are headed for an impass soon and it is probably better to not be under contractual obligation to them when you get there.
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