I am more puzzled now.
So if you use that glue, a thick layer putty won't crack?
In the big area (not the join) it is also a chance that the putty will crack because the foam is somewhat flexible.
I haven't seen the glue before, can you tell us more about it?
Would that be a rubber-based glue? (white color, smell awful?)
How fast it dries?
I was thinking about using a bit more of glue gun, and let the excess become the guide on how thick the putty will be.