You've got a big mess going on there, it's time to pay someone else to fix their mistakes, or start busting your GC's head to get him to do what you paid him to do! I assume you have a contract? If you are paying good money, then you ought to have something to show for it, and you should take this guy to court if that's what it takes! 2 months after installation and the unit still isn't working correctly? That is a joke, and he should have been forced to open up the walls under warranty and replace the unit and redo the finishing under warranty if that's what it takes. Didn't he or the plumber test the unit? It's your $$$, you should demand to speak to the plumber.
Anyways, the first thing you should do is call Delta yourself and get the ball rolling by explaining the problem to them. You say this was a new installation with copper? Who knows, maybe they loaded up joints with so much solder that it is causing a blockage. 0.5" copper is adequate for your installation, so there shouldn't be a pressure problem because of undersized piping. Maybe you have a defective unit from the factory. Simplest thing you can do is remove your cartridge and turn on the water and see what kind of pressure you have with hot and cold going full blast. The fact that your diverter isn't working means something isn't right. But it could be something as simple as them leaving the filter screens in place and now they are blocked, or the cartridge is clogged.