I've used the 2" 10lb density foam for an engine box and it really helped quiet down a pair of cummins 6bts.
The thing I really like about the 10lb foam is that it routes very nicely with a 1" roundover and gives a great finish and allows the glass to layout really easily on the edges. Any density foam should be capable of that though.
I never thought to use nidacore for an engine box b/c it is hollow inside it's cells. I didn't realize it was known for it's sound deadening properties but it would definitely be light weight.
I always assumed that epoxy would melt foam like this (ever put PL 400 adhesive on it?).
Is the Tuffr made from polyisocyanurate or the white popcorny foam like coolers from the beer distributor? I would check the compatibility first or at least find out what people are using.
The foams I am familiar with for residential use have very little strength. A 2" thick sheet is easily broken by hand foil on it or not but would have to assume if you glassed a whole box inside and out would be plenty strong.