If they entered your order into the GM Workbench system when you placed it (at the end of Feb.) instead of procrastinating, then the original price would have been price protected and neither you nor they would have to pay one cent more than the old price.
If they did procrastinate and did not get you into the system until after the price increase, then show them the email and tell them to stick to their word.
If they refuse to have integrity (which may be the case since they lied when they told you losing $3200 would mean no profit for them), and if you can afford the extra $3200 out of pocket, tell them you want to speak with the General Manager. Nicely tell him everything, then tell him that you will pay someone else the new full price before you pay them $1600 extra than agreed. Let them know integrity means more to you than money, and finally remind him you would prefer a long-term business partner including service for as long as you own the vehicle.
If he is reasonable, you will get the initial price you were promised. If not, tell the BBB that they refused to honor their email agreement with you, then never look back.
That is my $0.02.
On the other hand, if the added wait of going elsewhere, or the new full price is too uncomfortable for you, then, if you do escalate to the General Manager, stop short of telling him you will go elsewhere. In this case, you will have much less leverage, and need to be bedfellows with crooks to get what you want in the time and price range that is acceptable for you. Wash repeatedly after you get back home.
Those are my other $0.02.