Thanks to Fred, Harold and Mark who replied with ideas to fix the "9 Little Pollacks" painting, and this morning I worked on it as follows: I used a chisel to remove all the old glue material, sanded the surfaces, wiped it with alcohol to be sure it was clean and applied the contact cement. I can't tell you if it worked or not as I'm reluctant to stand it up to see what happens. I'll let it cure a little longer first.
Update: I had to work on this for a while longer, the second coat worked mostly but I had to clamp it for another day to achieve perfection. It is a very heavy piece and I'll put two hangers on the wall when I hang it.