4. Ditch team building gimmicks (see #3 for what's important).
I'd say gimmicks aren't going to save you, but consider morale events and other subtler stuff to help build team cohesion. Things like going to lunch regularly together, for example. When people are more comfortable with each other it makes it a lot easier for them to collaborate, rely on each other, ask each other questions, mentor each other, etc.
Wow, you hit the nail right on the head. Being a dick to someone trying to earn a living does say a lot about your character.
Cold calling someone is being a dick to someone trying to earn a living. Period.