Your biggest problem is going to be the lack of choke on a gun designed to clear a room and not take things out at a distance. Steel and tungsten loads tend to pattern better with lesser amounts of choke, steel "T"s might work out to 40 yards but tend to lose energy pretty fast. The other option is to fill the pattern you have with smaller shot, Federal 1 7/8 oz. copper plated BB's are a deadly number.
I shoot a 2 1/2" 16 ga. for coyote hunting and have experience much the same problem. Not so much the lack of choke but the limited payload as I can only load 1 oz and keep pressures and velocity balance in my 90 yr old gun. Nickel plated BB's fill the pattern and have plenty of Umph for coyotes, NP "F" didn't fill the pattern enough.
30 yard coyote 1 oz BB the shot completely penetrated the coyote either under the skin on the far side or passed through.

Patterning loads is the only way to find out what works as it seems with large shot every barrel has it preference.
You can get that barrel you have threaded for tube, a couple tubes and shipping for less than a new barrel You might check around, GB, Ebay etc. for a 21" 870 Express turkey barrel.
y 21" 870 Turkey gun that is my dedicated predator restricted area rig where I can't take the drilling.
