It just dawned on me that your medium is normally not foam hand puppets but marionettes. Are we talking about adhesives for foam or wood?
For foam

Generally speaking I make what clients are willing pay for

I mean - puppetry or sculpture related stuff

I posted a couple or foam's projects on this forum
http://puppetsandstuff.com/community/index.php/topic,6395.msg57413.html#msg57413http://puppetsandstuff.com/community/index.php/topic,6670.msg60118.html#msg60118It's only a few examples of foam's puppets

Once I wanted to learn more professional way to build stuff so I (
sorry for soooo much " I " - my English vocabulary is poor 
) find a mascot company which was looking for a foam carver and I was working for a few months here. They use air compressor and spray gun for contact cement so the process and result a bit different , anyway, I have kinda obsession with a quality of materials and always looking for "the best"

my questions here are result of this obsession

BTW my faworite fabric glue is Gutermann . For some reason it isn't for sale in North America , I order it from Europe
http://www.etsy.com/search/supplies?q=gutermann%20glue&view_type=gallery&ship_to=ZZ&min=0&max=0