Sorry if I'm repeating others' thoughts. I just ran out of gas trying to read the entire thread. Here are my thoughts on the matter:
1) I am assuming your bid on the job was a fair and reasonable bid. If you accept a lower price, you will get the job - the customer feels "empowered." That's the politically correct terminology, isn't it . . . when the buyer feels like he's mounted you . . . Alpha dog and all that stuff?
Well, four and a half decades of business experinece tells me you are going to lose TWO customers - the first customer, the one who paid more for a similar job, and the second customer, the one who now knows you were trying to screw him by asking too much in the first place. Yeah, even the Alpha dogs are discerning enough to realize they're dealing with a questionable supplier.
2) I am the owner/partner in several businesses. These ventures have always started slowly - no razzmatazz; no B.S - just word-of-mouth that I do everything I say I'll do, and I do it better than my competition. When the competition comes to my price, I raise mine. I'm worth it. I don't do marginal jobs, and my customers don't get marginal work. When I want to do the "negocios" thing, I head to old Mexico.
3) I learned one thing well as a teenager. I had a "garage band." We played for $300.00 a night. When the band got good, and we were in demand, a friend asked us to play his graduation party . . . for $200.00. We did it. Guess what our top offer was for the rest of the band's existence. You got it, $200.00. When we took a job for less than our worth, we doomed the band. I've seen numerous businesses fail for the same reason.
Just my thoughts. If somebody else gets the job for $400.00, you haven't lost a thing. If a competing bidder takes the original job, too, and if your bid was fair and resonable, your competition will fold under the burden of marginal profits. You'll end up with both jobs. One of my businesses increased its volume by 40% last year without a single sales call, just word-of-mouth . . . but for the seven years before, I did what I said I'd do. At a fair price. Better than my competition. This business is about to double in volume this year. Again, no sales calls.
A more reasonable approach would be to go to your first customer, the PROVEN customer, and tell him you have been offered a similar job. Explain to him that if he and the unproven customer can arrive at a schedule convenient to you, this will result in a lower price for both of them. Chances are you'll end up with him, the jerk who's trying to deal you out of 50 bucks, and a neighbor on the other side. The jerk will probably not provide you with a lead to his neighbors - jerks aren't trusted, even by other jerks.