Not saying I won't get a trapgun, but this week I worked on the attached.
1) Replaced hard rubber recoil pad with $25 Limbsaver pad. Reduced weight almost an ounce, but it's way softer
2) Added almost 15 oz to the stock for a net increase in gun weight of 14 oz.
For the stock weight I found that 3/4" steel tube from home depot fit beautifully in the hole (shotgun shells actually do not--just a touch too wide). I then emptied the shot from a bunch of cheap target loads.
I taped the end of the steel tube with foil tape I had on hand, standing it on one end. Took a tuna can, bent one edge to make it sharper for pouring, put a bunch of the lead shot into it, and took a propane torch to it (outside!). The shot readily melted and poured into the tube. The reason I melted the lead is that spheres in a space only fill up around 2/3rd of the available area and I wanted maximum density.
Haven't tried it yet but it's only pulled the center of gravity of the gun back around 1.5". It feels noticeably heavier and I think combined with the pad should work well.
If I want more recoil reduction I will attach some weights further forward. Even if I only use it for slugs down the line the extra weight and pad should make shooting them a better experience.