I have been shooting the 200 Accubonds for a few months now in .300 Win and Ultra. I tried H-1000 and 4831 but got my best accuracy with H-4350. You might consider trying it also - my rifle shoots 65-66 grains but you could work up to that.
Often the powder that's the MOST acurate at shorter ranges is the powder that is a bit faster, and ensures complete burning before the bullet leaves the barrel. The reasoning is that the bullet get buffetted by the "blow-by" of the powder gases as it leaves the muzzle, and the faster powders have lower pressures at the end of the barrel and hence less "blow-by".
At longer ranges velocity becomes a bit more important to maintain through winds, and hence more emphasis on slower powders. You'll also see that along with the slower powders people go to longer barrels to ensure complete combustion of the powder.
Noted that the military settled on the reloader series, Re22 in particular, for their A191 loads for the sniper rifles...gave the most consistant velocities and pressures over the widest range of temperature variations as well a keeping pressures within the SAAMI specs.
I heard that part of the decision to switch to that powder was the fact that Alliant Industries is now operating the army's ammo plant in Utah and naturally want to use their own powder. Alliant Industries is a huge conglomerate that happens to share the name Alliant with a powder comany that they happen to own. Regardless, it is no doubt very good stuff.
I've been playing with my 300 win Mag and the 220SMk's. I've tried RE 22, IMR 7828, H1000 and Retumbo now. So far my gun likes the H1000/75.0 grains, win cases, Fed 215M primers. Just shot 9/16" group at 200 yards (three shots) last weekend. The velocity spread was 2 for the three shots. This is a factory winchester rifle. Velocity 2689 at 70 degrees.
I thing I'm done with the load testing, now going to move out to the 1000 yard range and test some more for groups.
One of the top 1000 yard shooters last 4 years shoots a 300 win, 210 Berger and H4831 and wins more than his share of matches and national titles, so 4831 is a highly accurate powder with 200 gr bullets in the 300 Win mag.