Alan F,
Sorry but a bit of this is conjecture on all of our parts. Of course the OP asked what peoples opinion were and what recourse would he'd have and so on. But it has never sounded like he is remotely to the point of litigation and any intimation of such to me at least read as just a look down the road at a worst case scenario.
"There is a cost in both money , time, and personal energy in pursuing a claim. There is also the lack of funds for any of the work while this drags on."
There is also a huge cost in setting a precedent with a contractor that they even remotely have the ability to get over on you. It sadly reads as an adversarial relationship but its unfortunately something to be conscious of. I personally had a phenomenal salesman from one of our vendors that we nearly lost because he had several contractors who would call endlessly while driving (they have nothing better do do), call late at night (again), call on weekends (again), and when the salesman finally stood up and said to one of them "hey, I have a family, and I want to go to a little league game, a girl scout meeting, and so on, who do you think Im going to prioritize?" The instant response from the contractor was "me!"
Its all a give an take. And no different than anything, if your finding its all take, its best to cut bait. OP already said he is not counting on future business, sure best not to cut off your nose to spite your face, but perhaps there were several indicators throughout the process than sent up red flags.
"Devils advocate the first question the court will ask will be why did you assume the 40" was the overall height."
And answer is flatly and completely unarguable... "I didnt ASSUME anything, thats why we provided a detailed and dimensioned shop drawing and submitted it for APPROVAL from my customer".
"So I say settle and move on"
Couldnt agree more if you are dealing with a good customer (or even perceived good). We have customers that make mistakes completely on their own and we ship replacement material because they also work with us when there is a miss. They dont try to pad their bottom line with a $500 bill for 3' of molding around a leg they fouled up. I would venture to guess if the contractor had said "its our screw up, will you make the molding, we will install, and we will call it even?" It would have been a yes.
Tossing away money, and tossing away future work, is easy when your in a good spot, and miserable when your grappling for every penny. Kinda sounds like the OP would just rather get a check in hand and in the bank. We have all been there.