I have several factory rifles including Remington M700s, A BDL, two Classics and did have an ADL. Sold the ADL to a friend to give to his son as a Christmas present. The ADL was a 30-06. Mine came with a wood stock but I believe the OP's rifle has a Tupperware stock.
The idea if filling the forearm with bedding material is good but does add weight. I had a Mauser that I bedded into a Butler Crfeek stock that didn't shoot all that well with average groups running around two inches. I used modeling clay and built up two short towers inside the hollow foreaamd and pressed a 3/8" threaded rob deep enough into the clay so that the rod didn't contact the barrel. I placed two layers of electricians tape on the barrel, coated the tape with wheel bearing grease (very thin coat) and used an insulating foam material that I got at my local hardware store. I partially filled the forearm with the foam and quickly place the barreled action into the foam filled forearm and tighten the stock screws. It helps if you have someone help with and extra pair of hands but you can do it alone. I let the foam cure overnight and removed the gun from the stock. Don't forget to mask off the outside of the forearm as there will be overflow of the foam. The barrel should also be greased all the way around. No holes left to be filled and that forerm is as rigid as if it were solid material. I also used the foam to fill the hollow butt so it doesn't "boom" like a drum should you bump into somethimg.
One caveat. I have suggested this before and at least one person said it caused his stock to soften up and sag.
I've done this to two Butler Creek stock and two Tupperware Winchester stocks with no problems at all. Haven't done it with a Remington stock and never did find out who made the stock for the fellow that had problems. All I will say on that is it worked for me.
On barrel break in? Methinks it's not all that necessary and have not bothered as I consider it a waste of components, especially now with them so hard to find. Both rifles are customs with new barrels (Douglass). The .280 Rem. has had just about 80 or 90 rounds and groups are in the .50 to .75" range. The .308 has only had one box of factory through it and one box of handloads and it's doing .75" to .80" sor far.
The late barrel maker Gale McMillan stated IIRC right here on this forum many years ago that if someone did a barrel break in procedure on one of his barrels he would null and void the warrantee.
I've only had one rifle that fouled so badly that something had to be done and the fix was a shortened firelapping session. It's a great shooter now and the rifle, an M70 FWT in 7x57 is one of my favorites.
Paul B.