HVAC turning off below 30 degrees
What can I say ; you need to find a real HVAC guy to trouble shoot your system. Most guys today are parts changers: I know I have had them in my house.  Of course the problem is in the duct work since the installing  company can recoup their expenses with something they can charge you for. Is the new system a lot larger or about the same size as the old unit. If it is about the same size, you probably do not need any new duct work unless the old ducts are grossly wrong. They should have checked this before the quote to replace the unit. I would ask them to have "factory service " called to trouble shoot your system. On a separate note; what type house is this unit installed in? Since I am not there I can't say exactly what is shutting off the unit but I would start with the limit switches.