Wow. Nice long thread. My experience:
1. Use the lead sled after mounting a new scope on new rifle. I only use the lead sled on my .375 RUM, 300 RUM and other kickers. Put it away after that. The lead sled has too much bounce in vertical, horizontal and about 4 other dimensions to shoot groups that matter. You are inducing additional variables into your groups that cannot be eliminated. (I love my lead sled, but only for this.)
2. Use a front pedestal and rear pinching ear type sandbag or lead filled bag to shoot groups. Use this on the ground or on cement bench. No card tables or tailgates of trucks, please. This will eliminate most of the variables induced by lead sled. You do not need to spend a ton on a front pedestal. Any that has a front bag that reasonably fits your forearm is better than lead sled. I bet this combo cuts your groups in half. 3 shot groups to start to find some loads, 4 shot groups next on the good ones, then maybe 5 shot groups on your 2 best loads.
3. Save up or sell your 721 next year and get a newer Remington 700 action in caliber of your choice with the longest barrel you can afford. Even a used SPS or similar will shoot. (Case in point...son's new Reminton 700 varmint in .308 shoots .5" groups all day long and it only cost $425 at Sportsmans Warehouse. More cases in point....every 300 RUM in a Remington 700 action...I have worked up over 7 of them to date...can be made to shoot .5" groups. Worst has been .75" groups. All of them like Nosler 180 Accubonds, RE-25 and Fed primers).
4. When you burn out your barrel on a Remington 700 action, every decent gunsmith can chamber a new Krieger or other barrel on it that will continue to shoot .5" groups. Each Remington 700 action will last through several lifetimes.
5. If you can afford next year, get a stainless or XCR Remington rifle. It will go nicely with your Krieger barrel after you have burned out the factory barrel.
6. A scope with a little more reach will greatly cut your group size down. If you can obtain a 14 or 20x scope etc, so much the better. (Not necessary but fyi, we use old 36x cheap fixed power scopes work up loads, then remount our "hunting" scopes.)
7. Brass type or prep or weighing, bullet type or brand, powder or primer will not matter unless you start with the above.
8. Accubonds, Ballistic Tips, Combined Technology from Nosler will all tend to be much more consistent in the groups than Partitions. You will get flyers with Partitions and I do not care if you are shooting a $4,000 Bat Action 1k rifle. However, Partitions will kill an elk just as dead as any other.
9. For another weather variable I would eliminate would be on the powder. Use Extreme powders. H4831 etc. see Hodgon website. (That said, I use RE-25 on my RUMS because it shoots tiny groups.)
10. If you are using the 300 H&H for nostalgic purposes, go for it. I do that with my Dad's .308 with an 18" barrel and totally get that. Otherwise, next year....there is a reason the military snipers use 300 Win mags on Remington 700 actions...they shoot.
11. Make sure all the screws on your action, scope rings and mounts are tight.
12. After you find your load for the 300 H&H, go shoot at something at 400 yards as you would an elk. Milk jugs, 2 liter bottle etc. How did you do? That 9 power scope kinda makes it more difficult. That said, an elk shoulder is pretty huge at 400 yards even on 9 power. I hope you shoot a record book elk if you have not already.
There. I feel better. 12 steps to help one of my bretheren.
Best,
Somerumbum