HI Bart...If you're going to rivit the pieces together try to keep the same dimensions as the foam you've cut...Here's a few options off the top of my head...One route would be to rivet the end without the foam inside..Keep the dimensions tight so the foam will have a resistance fit going in...
Second thought would be to assemble the unit as you've pictured and use 3 or 4 small ratchet straps to pull everything together snug before riveting ...You could possibly make up some wood spacers shaped like the foam for either method if need be..

That being said the foam is simply to keep the sheeting from drumming it really does'nt need to be extremely tight...The top and bottom end caps will hold the shape...