ok.. I would leave 1-2" on each side of the bench at the top and cut down to the floor, but leave about 1-2" above the floor as well. You can still have the whole middle pretty much gone, but leaving that little bit with still leave you some reinforcements for the sides. Go ahead and take all of the foam out, taking it out is not going to hurt you any since you are taking out pretty much the whole bench anyway.
Just brace the cutout on the sides and the floor with 1/2-3/4" ply, then I would raise the floor infront of and behind the middle bench you just cut out so that it is all level. You can run 1x1 square tube perpendicular to the ribs from the back bench to the middle bench, then from the middle bench to the front of the bow. Just cut the middle bench down to what would make it level across from the rear bench to the front of the bow, then put you one 3/8-3/4" sheet of plywood for the floor.
You might also think about cutting the bench sides at an angle so that you can use that as a "built-in" brace, and attach that back to the flooring for side strength.