I’ve never worked on an ebody with an overhead console, I have a friends SE Challenger in the shop and my question is what type of adhesive should I use to glue the foam backed felt to the headliner board. I’m a little apprehensive what to use because I don’t want the glue to melt the thin foam behind the new felt he has.

Good old fashioned contact cement. That's what it was made for (well that, and Formica).

If in doubt, use a few cans of 3M Super 77, but contact cement is the product of choice. Spray it on from a cheap gun. Lacquer thinner will clean it up.

Works for me, I'll give it a try. thx.

I've used contact cement several times with great results.

I did the headliner on my 95 Eclipse.
It was an aftermarket headliner material with felt material and thin gray foam backing. I used 3m FOAM spray glue. There is also general 3m spray glue but they must make the foam version for some reason. I got it at Advance auto for around...14 a can if I recall. Home depot used to carry it but I had trouble finding it last time. Took me 2 cans...and my headliner is smaller than yours for sure.

You want good coverage. I used 2 coats and criss crossed the 2nd over the first in the other direction. DON'T try to coat it heavily with 1 coat!! I did in one area and it saturated into the foam and ended up with a flat spot. Luckily it was near the edge so it's not noticable.

Follow directions on the can and you'll be ok. It helps to have 2 people to lay the headliner in place to ensure it's laid down evenly.

BTW...I got the headliner material on sale. The 2 cans of glue cost twice as much as the headliner...