For quickly gluing balsa strips or sheets to expanded bead foam with Ca, I've been using acetone in a spray bottle. Spray the entire foam area and let dry to form a glazed surface. Using MEDIUM Ca, it will glue the balsa to the foam without the usual meltdown. Try a scrap sample to get the feel of how heavy to spray the acetone and the amount of Ca. I've used both the thin and medium Ca, but prefer the medium for sticking down cap strips along with the leading and trailing sheets. The one time using the foam-safe Ca, I wasn't happy about the price or the shorter use life once the bottle was opened.

Pardon the repeat if this tip has been posted in the past.

But acetone would melt styrofoam...

Hasn't yet, try it.