Today I trimmed and attached the panels, leaving a hole to spray in the expanding foam. I attached the panels with a gap of the panel depth, the reasoning behind this will become clear later on. I used a variant of "No More Nails" to attach the panels.
After the panels dried in place I sprayed the whole can of expanding foam into the gap. In hindsight I should have only used half the can, as I had to clean a lot that kept coming out as it expanded.
I'm quite pleased with the end result, it sounds solid when you knock on the panels.