You could always sell the mossberg and buy another barrel for the 870 so you will have a turkey barrel and a wingshooting barrel
Exactly what I would do.
I have an older 870 Pump 12Ga express mag w/20" barrel, w/Rem xtra full turkey choke. I shoot 3" Federal turkey loads #5. It patterns best in my gun with these loads. I have tried many others and thought I had it patterning good with Hevishot, until I tried federal and it just worked best for my gun. Each gun is differant though and differant chokes and ammo brandsmay patterndifferantly in each gun. I pattern mine to 50 yds and it is good, although, ashamedly I do admit to taking a bird last year at 73 yds. It was a spur of the moment shot and I would not have taken it, had I ranged it was that far.
I also have a new870 in a 20Ga with the exact same barrel for my daughter.