I used H4831 for years in my 270win and only shooting 130gr bullets (Nosler Partition and AB). Then I started Moose hunting and loading 150 Nosler Partition, I had some IMR4831 and gave it a try on the 150's and I get much better groups than with it the H4831sc. Of course that's in my Tikka...
My wife has been killing Turkey for about 40 years using a Remington 870 and just plain #5 shot. All through a few years ago she's stop using 3" shells. Oh yes, she owns two different 870's. First 870 has just Mod barrel newest has select Rem chokes.
I've found 180 Accubonds are more accurate than Partitions. Not so much that it would make a difference shooting a Moose at 300 yards or less. But I think Partition are better bullets.
One of my hunting buddies has killed two very large Moose. He uses a .308 with 180gr Nosler Partitions, I don't know his load. I think it's his calling that gets the Moose, he is also the best shooter I've ever meet.
I've killed 9 deer with XTPs 200/240 & 300. Two from muzzleloader 240's the others were from a Ruger Redhawk with 7 1/2" barrel. I seen no difference in the three weights they all killed quickly.
I've been shooting Turkeys for years with my 12ga 870 and 16ga Hunter Fulton and I don't use anything special just #4 or #5 shoot. So you might look for regular shotgun shells.