Are you looking for tighter patterns?
If so, it would be cheaper to switch ammo to something better than S&B. Any of the usual suspects where cheap buckshot is concerned (S&B, Rio Royal etc) have dead soft lead pellets, that are poorly protected in firing and their trip down the bore. You want wide patterns, that list of qualities should give them to you. And adding choke may or may not do much to improve that situation.
Major manufacturer 'standard' grade buckshot will usually give medium sized patterns - Remington, Federal, Winchester, Fiocchi etc. Costs a bit more, but ... you get harder alloy lead pellets that are better protected with shot cups, shot collars, plastic buffering etc, which is where the better patterns basically come from.
And if you want the tightest possible patterns out of a CYL bore, get some FliteControl stuff - Federal Premium or LE, Hornady TAP etc. I have one 870P 18" CYL barrel that will deliver 4" patterns of Federal LE127 00 at 25 yards. And that isn't unusual. These loads feature very hard alloy pellets and/or plated pellets, excellent protection in the bore, and the amazingly efficient (as long as you don't use a wad restricting choke) FliteControl wad.
Or, Remington makes a 18.5" RS barrel with tritium sights and a factory fixed MOD choke, for reasonable money. Worth thinking about IMHO, especially given the current ammo situation.
And NEVER "assume" anything about what a given barrel will do with a given load at a given range. PATTERN IT and find out!