I tryed the steel rods and arrow shafts in the forarm of a Savage FV many years ago only to give up and put a $79 laminated stock on it. The only way you are gonna really stiffin up a Stevens stock is to put the shafts on the outside and blend them in, otherwise the forearm will be stiff but it will still flex @ the recoil lug!
As for weight you can do like someone else said and drill a lot of holes in the forearm and fill with lead shot and epoxy. Put a bread bag in the stock and you can fill it up with whatever and take it back out if want/needed.
After being down this road more than a few times I would just make sure the stock is not hitting the barrel and bed the action in, put on a better recoil pad and shoot the thing till you are good at it. Naw thats a lie I would butcher the stock and revamp it to whatever I had on my mind at the time, god only know how it would turn out
Not a one of my Savage/Stevens are bone stock, some only have been bedded and trigger worked over while others are complete redoes from the action out
This little Stevens started out life as a 223 but is now a 204. I cut the forearm down to the checkering and moved the bipod stud back 2½". It now shoots off the bipods a LOT better. I will add a better recoil pad after the doggin season this year and put a 708 barrel on it for an easy carying goat gun...unless I give in and just buy another Stevens with a .473 bolthead???