my first season I used my 870 with a remington extended "super full" choke and killed a 20 lb. Merriam's with Winchester Supreme 3" 1.75 oz #5's. this tube was probably ~ $15.
if you pattern your factory full choke tube with those #5's or #6's, you may find that it will work out to a killing distance.
my old 16 ga. fixed full Model 37 shot decent patterns out to 35 yards with Win 1 1/8 oz #6's.
sorry poor quality pic.