That's what I was going to suggest, too. I've got a 1X-by-40mm BSA on one of my pellet rifles. It was cheap (~$35), and has good eye relief and a broad field-of-view. It's cheap enough that if it breaks, I'll just get another one.
No matter what sort of scope or barrel or sabot slug you use, no shotgun is going to be a tack driver. It's worth a try for a few bucks. Just remember to turn it off when you're done. The battery is supposed to be good for 200hrs, and I haven't managed to wear mine out in the past year.
