Minecell should be softer. I would double check as there are different "grades" of minicell. All my cboat converts use this and I find it quite cozy.
Now, if I can get my leg to stop falling asleep..
Contact cement is toluene based. What you need to do is apply a coat to both surfaces allow it to dry, ~ 10 min or so pending temperature. Then apply a second coat to both surfaces, again, let it dry ~ 10 min or until not tacky. The fun part is laying your foam on, its more or less a one shot deal in most cases, sometimes you can get away with peeling it back up, weight it down and leave for 24 hrs. I use Weldwood C.cement and it has worked pretty well. Just make sure you really work the glue into the foam. The solvent shouldn't destroy the cooler, leave it right side up, or else it will. The fumes need to escape through the foam. Many canoes have been destroyed by flipping them upside down to allow pads to dry.
A wealth of links and info for you :
CBoats.net - C1 B1!