I just bought a used Model 70 Classic Stainless in 375 H&H (synthetic stock). The gun is a little lighter than I prefer.....and is very barrel-heavy. I would like to add a pound or so of weight to the inside of the stock (in the rear).

What are the best options for doing this (preferably cost-effective options)? Should I use lead or some other material? And what type of glue/epoxy should be used for maximum durability?

I was also thinking of filling the entire hollow area of the stock with expanding foam after the weight is added. Are there any reasons why this should not be done?

Thank you in advance guys.

First off you could add a mercury recoil reducer in the butt stock and that would add just about a pound of weight and give you some recoil reduction as well.

Other option would be some #9 shot mixed with epoxy and poured into the stock then add some more epoxy over the top to be sure it's covered and sealed in place.
Then yes fill with foam.

Either way you should get some double sided tape and some solid lead weight to get the balance right. Just adding weight will not fix the problem Adding the correct amount of weight and in the correct spot will.

I added 1.5 lbs to my 416 by class bedding it with a bunch of lead shot added to the bedding compound.

One could do the same to the butt stock. If one wanted to make it removeable coat the inside of the stock with release agent.

Have you shot it yet? You might be surprised as the H&H is not a beater in the recoil department IME. For a number of years I hunted with an early Rem M700 Custom Shop KS that, with the barrel cut back to 21" and scoped with a Leupold 2.5-8X, weighed a hair less than 7 3/4# IIRC and it was not a problem. I only shot 260's and 270's.

Well if he's asking for only one additional pound I don't think he's worried about the recoil. One pound would not make a difference in recoil reduction.

It's more of a balance a fit issue for the post.
He said Barrel heavy. and that can throw off how a gun comes up and mounts to the shoulder. I have one rifle that fits me perfectly and is balanced correctly. It is the fastest rifle I have for getting on target. fit is smooth and the balance is perfect. As near a custom fit rifle as I will have anytime soon

Mine is just like what you describe, stainless synthetic stocked M70 classic 375 H&H; previous owner put a merc tube in buttstock and it balances great for me. Also seems to recoil less than it's twin in 300 WM.

I had a Hogue that I added about a # mixed lead shot in epoxy added some in the front and also the rear followed by spray foam in the rear.

After you add the shot/epoxy fill the void with plastic grocery bags....just stuff them in.
They do a better job than foam in dampening the hollow sound and in time can be easily removed if you want to add/subtract weight.