hello!
In our shop we have replaced HVAC control heads on these vehicles to cure similiar problems. We don't see very many BCM failures on these models though.
Usually, diagnosis of this type of fault is pretty easy IF a tech can happen to catch it acting up when a DRB_III scan tool is installed; otherwise they often leacve no clues as to what has happened.
The $600 you are being quoted for a control head assy seems pretty steep. According to my estimating software, if you have auto temp control on this model the price for a BRAND NEW one from Mopar is $445.00 (part # 4596005). Often, there are reman units available through chrysler also. You will also be able to find these in salvage yards for less than $100.
Replacing the control head is very easy and takes about 15 minutes. Just remove teh trim plate from the dash, remove teh screws holding the control to the dash (4), unplug the electrical plug, and reverse to assemble. There are no cables, hoses, or anything else to deal with; it's very easy and you can do it yourself with no special tools (just a socket set and screwdriver). No programming or scan tool is needed to replace the control head.
I hope this is helpful to you; if so, an accept would be most aprpeciated! Thanks!