Post a couple of pics if you can so I can see what area your attempting to bond.

You can use any of the super glues available just sparingly and don't use any kicker. The way it works creates a lot of heat that will melt the foam.
First thing, and it can be a pain, is to scuff both of the areas to be bonded and then clean them with alcohol. Let them dry and then use CA although "sparingly". Too much and it stays wet and takes too long to dry. My typical method is as described though I usually use thin CA and while pressing the parts together I wick the glue an area where they are touching as you mentioned. I also use those sharp point tip caps that go on the end of the bottle. That way you have a lot more control of how much glue comes out.
I'm in Tulare just a couple of hours north of you so if your ever my way or im down there id be happy to show you.
Shoot me an email if you need [email protected]
Paul