3M's Super 77 is a fabulous spray glue to use - though really environmentally unfriendly - BUT if you are using it on foam it is really only good for gluing fabrics to foam. If you don't use the right type of spray glue for foam to foam gluing either the foam will fall apart eventually or not stick at all.
If you are looking to glue foam to foam you need to purchase a specialized foam-to-foam-adhesive. I know LePage makes the one I've used, but I can't recall it's name. I haven't tried the 3M 74 spray, but it sounds like that may be 3M's foam-to-foam adhesive product.
It's really important with contact cement and spray glue that you make sure both pieces you are gluing together have been sprayed or glued, otherwise they'll eventually come apart.
It's also very, very important to wear a proper respirator and protective gloves when using spray glue and/or contact cement. Even if you are outside or the fumes don't smell strong you will still be exposing yourself to very toxic chemicals.
Safety first!
Puppets aren't worth killing brain cells for!