NO!
save the fmj rounds for shooting through steel, they are not a hunting bullet.
And 7/8" @ 200, that is under 1/2moa, factory gun and factory ammo, you should go buy a lottery ticket.
You are trying to solve problems you don't have, you have a great thing going there, go ahead and try some hornady TAP 110'S for fur, but at the end of the day, you've found a [beeep] of a combo already.
Good hunting.