JimG -- a forcing cone job involves lengthening the forcing cone (see Foggy's explanation). I had it done to my trap gun, and it did even up the patterns some. Should yield even better results in a .410. But -- the .410 is a finicky creature, particularly the 3". You are asking a very long shot column to produce an even pattern at 20 or 30 yards, and the only way to do it is to baby the shot as it passes from the shell through the narrow little bore and the choke. A shallow forcing cone angle helps a lot.
Another thing to consider in .410 ammo is the hardness of the shot. Most everyday shotgun ammunition is loaded with shot that is only slightly hardened with antimony. A handload made with 6% antimony target shot will pattern a whole lot better than most field-load shells. You can get high-antimony shot for handloading in field sizes (5, 6), but the only factory-loaded ammo that always has good hard shot in .410 bore are skeet loads, and they usually only come in #9.
If you don't handload, you might ask NEF if they will fit a larger-gauge barrel to your Versa-Pack frame. A 20 shooting 2-3/4" ammo doesn't kick much more than a 3" .410, and your ammo selection is much better.