First of all, we dig cookies. Peanut butter with fork marks are very well designed IMO. Never trust a person who won’t eat a cookie. Eating two cookies is preferred. Eating more than two is a secret. So I sure hope you ate a cookie or two (wink) before you called BS.
You have many litigation options, but suing everyone for everything is a poor way to go about your life. Try proposing a “pass-through” agreement, also referred to as a “liquidation agreement.” These agreements essentially remove you from the case by assigning your claims to the GC, who then can sue your design team and the GC’s own subs until the proper liability is apportioned between those who designed or built the HVAC system that is on the fritz.
Send your GC and its counsel some pecan sandies and let the negotiations begin, YouDig?