You might try something like this:

https://smile.amazon.com/gp/product/B01FKP4B4U/

I just used that on my Remington 700 and it seems to work well. The only concession is that I had to move some of the foam back to accommodate the long action bolt throw.

Previously I'd just used some high-density foam held on with hook and loop tape and covered in soft cloth, but this is a nicer package overall.