Stiffening the forend is a good idea. I use wrapped carbon fibre tube from the local hobby shop and foamed Gorilla Glue as it is way lighter than steel and epoxy. For a stock like that I would use 2 full length tubes. Inlet them into the bottom of the barrel channel trying to keep a tight fit. I use a drywall bit on my spin saw but use what ever you have. It doesn't look like much material to remove anyways so even an Olfa knife would do. Scuff inside the stock channel and the outside of the rods slightly. I use a small metal brush on the spin saw for the stock channel. Clean and degrease the channel and rods. Put a good bead of glue down, lay the tubes in the channels you made, spritz the whole thing with water and the glue will start to foam up. If your tubes are loose the foam will lift them so you have to hold them in place. Tight is better. I then put a layer of wax paper on top of the glue, I usually cut a strip of wax paper first so it is a couple of inches wider and a couple of inches longer than the barrel. I then place the action, sprayed with silicone spray in the stock and tighten down. If you have already free floated the barrel just add a layer of thin cardboard stock on top of the wax paper before you replace the action. I use stationary store card stock. Let it dry over night and then trim any excess foam away with a knife. Very easy to sand and re free float if you mess up a little.I then put a super fine coat of epoxy over the foam when I have finished glass bedding and you are done. Very light and very strong. I have done a couple wood stocked guns, Winchester Featherweights, and 4 of those Butler Creek synthetics that were so flexible you could probably tie them in a knot and they are all ridgid as steel now.
Kim