Stiffening the fore-end.
First a picture of a raw Stevens 200 stock. Same for all calibers as far as I know.
1. You will need a piece of 3/8" keystock - 9 1/4" long. You will also need a sling swivel stud, just like the existing one (Uncle Mike #2506-0). You'll also need a tap to match the threads on the sling swivel. And you also need some Lepage's 2 part epoxy (#12) again.
2. Remove the existing sling swivel and nut.
3. Drill a hole through the rear circle. This is meant to accept the 2nd sling swivel. Drill it the same diameter as the front one.
4. The keystock has to be fitted full lenght of the fore-end, between the two longitudinal rails. It will tightly squeeze in there. But, you have to remove the material from the cross-braces (marked X). The keystock must fully rest on the flat surface inside those two circular shapes which house the sling swivel. There's quit a bit of digging out to do.
5. Once the keystock can be fitted snuggly inside the rails, flip the stock over and through both stud holes, mark the keystock. Remove it and drill and tap accordingly to accept the threads of the sling swivels.
6. Before applying the 2 part epoxy, let's re-insert the keystock and thread the studs into the keystock. Tighten things up to make sure it fits well and that your swivels and nice and straight. With the keystock in place, drop the barreled action in, just to make sure that you still have a free-floated barrel. There should be a lot of clearance if the keystock is down on those two flat surfaces inside the circles. Once you're happy with it, remove it again.
7. Now, you will want to make sure that you have enough epoxy to fill that whole forend (minus the volume of the keystock of course). I use the dremel tool to rough up the surface of the stock which will be in contact with epoxy. I also drilled a few shallow holes into the keystock and some into the inside of the forend. This ensures that you have locking bonds between steel, epoxy and forend.
8. Return the keystock one final time in the forend. Screw the sling swivels in and tighten. Put a bit of plasticine into the top of the threaded holes in the keystock that remain exposed. This will ensure that epoxy does not flow in there and render your studs unremovable. Now pour the epoxy in, push it into hollows, under the keystock, filling all nooks and crannies. Don't worry about making a mess, these plastic stocks clean up well. Don't make a mess of your bedding job though. Have enough epoxy on hand to even go over top of the keystock to fully cover it. Not so much so that you won't have a floated barrel though.
9. Once things are cured, I pull the recoil pad and remove that styrofoam pad from inside the hollow butt-end. I then fill it with "the good stuff" foam insulation. Leave the stock sitting vertical butt-end up.
You'll see that your guns now feels very, very different. You'll like the change, I'm sure. Good luck.