My solution for this challenge was to go to Hobby Lobby and buy a stretched (& primed) canvas that painters (artists) use. It's 24x48 and cost about $17. That was cheaper than the canvas I was looking at. Anyway, I bought a 24 x 48 piece of pegboard (masonite), screwed it onto the canvas side, padded it with pieces of batting and stretched WET canvas over and stapled to the inside of the back (so the staples wouldn't scratch any surface.) I have an island in the kitchen that is 30x48 and that's where I'll iron the cloth. It's still heavy enough, but not as heavy as plywood, I think.
(originally I thought I could use the canvas side if I padded the back enough, but this isn't ideal on the 12x14 one I did. My artist friend assured me I could spray the primed canvas with an acrylic paint and could iron on it...not sure that was good advice!)