People in jigsaw forums usually recommend using transparent latex binder for glue. This is easy to use on top (use transparent binder!) and works great. I glued Educas Borras Life with it (24.000 pieces). Applying the glue on top is best. Anything on the backside is too much work.

As a warning I'd recommend to stay away from most commercial puzzle glues. Some of them are water based - and this doesn't go well with cardboard. Anything bigger than 1000 pieces will start to warp a lot.