I have a Franchi Affinity with the 26" barrel and same Mobil choke system as your 3020. I can't speak for the .555 as I never tried one, but I have tried and have a .562 and a .570. I also patterned a .575. I would not be afraid to hunt any of them out of my gun. I shoot the Federal TSS #9s. The .562 Sumtoy has an even pattern and puts an average of 310 in a 10" at 38 yards (as far as my back yard range will let me shoot em). The .570 - even tho more open, averages about 10-15 pellets more at the same distance. The .575 would drop me down to about 280-290. Any will be lethal out further than I would shoot at a turkey. I currently have both a Sumtoy .562 and a Jebs .570 for my Affinity. I have an 870 compact with a 21" barrel. I shot a .562, .565, and a .570 in it before settling on the same constrictions to keep. There was little to no difference between the .562 and .565 in this gun (between 290-305), but the .570 averaged around 330-340. So in both my guns using TSS, the .570 actually averaged more pellets in the 10" than more constricted chokes. I have the .562 Sumtoy and the .570 Jebs for my 870. So basically, I guess what I am saying is in my guns, more open didn't necessarily mean more open patterns....but each gun is different. Find ya some chokes on the 20 gauge chokes for sale section on this site and try em. I have a .570 on there I bought at a lil mom and pops store that was closing. Didn't need two of em. Good luck and you won't go wrong with either the .570 or .575 Jebs, or a .562 Sumtoy. Lots on here use the .575 Carlsons extended non-ported.