For foreend rigidity without the weight, try this.
using a forstner drill bit (allows you to drill a flat bottom to a hole), mill out the eggcrate reinforcements in the foreend now.  They don't do a hell of a lot anyways.
Once you have a flat bottom and sides, epoxy in pieces of 1/4 to 5/8" thick plywood.  If you don't mind the extra ounces, go full length.  Otherwise, space out every 2 to 3" inches some pieces that are 1" long by the width of the stock.
Make sure that the piece is well glued to the bottom and sides.  If you start under the recoil lug, you will help eliminate that vertical flex of the stock.  As you add pieces going forward, you will reduce the side to side and vertical flex.  The amount of torsional rigidity will also go up - harder to twist the stock.
It is a bit of trial and error to get it right and I have don't have many stocks to play with.
Another way is to make a piece that fits the entire length of the bottom then drill out some lightening holes.
Bondo and other non torsionally rigid fillers will add quite a bit of weight  for the rigidity they to provide.
Jerry