Well,
I have a 1973 J40 with the same symtoms. I had to do the following:
Remove the bindings, cheap cellulose binding. Use a heat gun carefully.
Separate the back with the help of the heat gun
Clean the top from old glue and re-glue it back and make sure it is positioned correct.
Use super glue to close cracks.
After I did that, I realized the stable was shifted. It is now in tune.
Glue back the back.
I went with two 3x7mm, black and white vinyl binding. Not original, but this model was the cheap of the cheapest Gibson produced. But I love it.
Oh, re gloss with cellulose lacquer.
