I would not flaunt the letter about how pregnant you are. It might come across as sounding as if you deserve to be upgraded because you're pregnant, and that's not going to get you anywhere. If flying in coach while pregnant was that much of an issue for you, the reasonable unasked question the GA is going to be thinking is, why didn't you buy a biz ticket in the first place?

I think your best strategy is to first ask if there are any exit row options available (be prepared to pay for E+ seating if that's the case) and, if not, if there's a reasonable opportunity to buy an upgrade into biz class. If you're in the company of a GA that for some reason thinks this ought to be your lucky day and you deserve to fly in biz on an op-up, this will bring that person out in the open... without the risk of sounding like someone who wants something for nothing and having all your options cut off.

And again, don't use that letter. I cannot see anything good coming from it, as far as flying is concerned. In fact, it could be bad for you, because it might convince them (and perhaps reasonably so) that you're not a good candidate for an exit row.