You do not need 3" slugs. Your shots are around 50 yds, and 2.75" will work just as well out to 100 yds. Switch to 2.75", unless your 870 has a 3.5" chamber.

A lengthy sight-in session with slugs is a waste of money and time for most guys, as you realize by admitting you may be flinching.

Make sure your mounts and rings are tight.

I shoot 2.75" 12 Ga. Brenneke KO Sabot Slugs (not the "regular" KO slug), and they absolutely hammer deer.