What type of plastic is the heater box made out of?

Problem isn't the material you're using,its age. The plastic Mom Mopar used back then wasn't all that "flexible" to begin with, and if this is a support post, you're prolly going to end up fabricating something with a bolt , a drill, and some rubber bushings. JB Quick in the tubes works great for most any non-support area. Good Luck!!

There are tests to determine the type of plastic that you are working with. A float, smell,scratch or flame test is used for ID:
http://globalwarming.ygoy.com/2010/08/15/how-to-identify-different-types-of-plastics/

The fusor adhesives are expensive, but very strong:
http://www.lord.com/products-and-solutions/adhesives/oem.xml

My favorite all-purpose adhesive for automotive interior bits is 3M structural adhesive. Seems to bond better than JB weld and cures quicker, but less brittle.

I have repaired all kinds of plastic no matter what type it is, especially the old stuff, by taking a soldering iron and gently melting wire the size of paper clips into the plastic. It is a little tedious to do, but it does strengthen everything good. Support both sides, lay the bent wire on the plastic, then take the soldering iron and press the wire into the plastic, which will heat the wire and bury the wire into the plastic, smooth the plastic over the top for appearance. Not real clean, but at least the part remains in place. I have done this on plastic grilles and interior parts for years.