67 barracuda heater core replacement

I just did mine, but I had the heater box on the bench. I would suggest just
dropping the heater box from the firewall so you can get to all of the clips
that hold the halves together. 4 nuts in the engine compartment around the
heater motor and 1 support rod on the passenger side that holds the box up to
the fresh air intake. When you get ready to put the support rod back in,
there is a nut on the bottom of the box. Loosen it quite a bit to make the
hook longer. After you get the support rod hooked on top of the large air intake
hole, tighten the nut on the bottom to draw the box up tight.

You could probably loosen that nut to drop the box down in the removal.
I didn't do that when I took mine out...didn't know it was there. I just
pushed the complete box up and unhooked it.

The shop manual shows this:




Hope this helps
.
.
.
.