During the meeting we talked about high density foams that could be cut with a hot wire.  Tim pointed out that there is a product that is very dense (no visible air pockets or variations) called REN Shape Tooling Board, or REN Board, or RENShape Board.  I contacted some of the suppliers and was advised that this material is too dense to cut with a hot wire.  It's designed as Tim pointed out to be cut with tooling machines.  

That said it is a very interesting material and could be used to make model bases as it is very consistent and cuts easily with the right tools.  

What you want to use is High Density EPS Foam boards or blocks.  The construction foam board "project Panel" I bought from Lowes works very well and is very low cost.  There are denser materials out there and can get pretty pricy.