E-A,
I've shot a couple #1's pretty extensively and a Pre-64 M70 in 300 H&H. I love both of them dearly. The 300 H&H might just be my favorite PG Cartridge of all time. Nah, I take that back - it is. No question. Color me a light shade of jealous with your rifle!
There are few things I've learned about #1's. I hope this helps:
1. The Forearm and Hanger puts pressure on the barrel. If you are shooting off a rest that can be a problem. In fact, that was my #1 problem with the #1. (*Pun intended!) The key I found was to make sure the rifle on the rest was right at the frame. I had to constantly remember to re-set the rifle after each shot on the rest. Push it forward until the frame juuuuuust makes contact with the forward rest of the of the rifle. Make sure it is exactly that way each and every shot. That's going to be the most stable and solid place on the rifle and that is critical to consistent accuracy.
PS: If you shoot from sticks, please make sure you take the rifle position into consideration. It would be really easy to set the rifle on the forestock or the barrel!
2. The hammer fall is longer and takes more time. No, really. Inside that frame is an actual hammer, much like a lever gun. It has a longer lock time and that lock time means there's a shade of a microsecond to affect accuracy. Trigger follow through is critical. You have to make sure you keep the head down and follow through on the shot.
3. The trigger isn't the greatest. On my 7x57, it was a bit long and 6# creepy. I added an aftermarket trigger and it made a notable difference. (*to be clear, consistent rifle placement on the forward rest made the most difference).
My 7x57 went from 2.5" groups to .75" groups when I got my technique down. I added a Speedhammer, a Trigger and a Hicks Accurizer. They do help...but too much pressure on the Hicks can split the weld on the hanger/barrel. And, in the end, it's not really necessary. So, my advice is don't waste the money unless the technique plays out right.
Now, onto more fun stuff: 180gr. TSX at 2850+ is all you need. Yes, you can dial it up hotter...and please, do so if you want! But really, it's just not needed. TSX, Partition, E-Tip, Accubond...they all work.
And the .300 H&H is truly all you need.
PPS: before you ask, what happened to my old #1's? I just didn't get along with the weight and wanted a lighter option. Still...if there was ONE #1 that I would own...a .300 H&H would be it. They really are that nice.