Sure, you could use the sinkers. I'd probably use something other than rags to hold them in place and prevent rattling. I suggested the expanding foam insulation because it will completely fill the void space and hardens very firm, but will allow the overflow to be neatly trimmed to make a very clean job. Once the recoil pad were reinstalled you won't ever know it was done, and won't have to worry about the sinkers or shot coming loose sometime later forcing you to redo the job later.

Mike