Just to add to what others said, definitely check out the Facebook Mopar groups as sometimes people part out these cars and you can snag good used bars that still have plenty of life left in them.
Those Coker ones look promising, worth giving them a call to see if they can tell you the exact depth before ordering. The previous set of custom wheels that I got from carid I was able to request a custom offset produced for my exact spec to fit the tires I wanted. It costed some extra, but...
I've seen guys use the Federal Signal PA300 controllers for shows - pretty straightforward wiring through the existing radio harness if your Diplomat still has the police wiring intact.
Yeah I'd stick with 5/16" steel line for that application, you can get good pre-bent stuff from Classic Industries or just get straight sections from NAPA and bend it yourself.
Sounds like your blend door actuator might be stuck or the vacuum lines are shot - those old Mopars are notorious for vacuum leaks that mess with the HVAC controls.
Yeah I'm with you on the confusion - seems like there's conflicting info on whether the J-body changed dimensions in '80 or if it stayed the same as F/M bodies.