I've fitted a couple of 12ga slug gun stocks to 20ga 1187s.
All you need to do is use the stock bearing plate in the back of the 20ga action (basically a washer contoured to fit in the receiver recess) as a template on the face of the 12ga stock tenon. Then using very sharp wood chisels or if you have time to spare an X-acto knife set, slowly shave the outside of the tenon until it fits the action. Don't take too much off at a time. Don't reduce the length of the tenon. Don't worry about the trigger recess - it will fit. The width of the stock will match.
The main difference is with the top. The stock will stand up slightly above the receiver. I didn't bother to reduce the height of the two I did. It's not noticeable unless you look real close. If it bothers you, it can be contoured to match, but then you'd need to refinish it.
If Tron has a 20ga action maybe he'd do it for a fee?