A 300H&H would be damn nice. I have a couple H&H action rifles as well. I don't know what mounts you got. Assuming weaver style, as those work great on these rifles. I started a thread last year on a rifle I put some Warne mounts on. I did that because I was a little irritated that the mount extended out over the front of the receiver:
I ended up cutting that base and then rebluing it. Here's the thread:
Mounts for pre 64 model 70 H&H rifles