I agree with you about the H&H being underloaded. I started experimenting with it this last spring using 300g bullets and H4350. I am loading it a lot longer than standard, as well. With 300g Hornady BTSP, I achieved 2720ish from a 25" barrel and Hodgdon BOOK LOADS. With 300g CE's, I got 2760+. I was getting zero pressure signs and felt that there was still some throttle left, but didn't push it because I had already exceeded what I was hoping for.
I haven't developed accuracy loads for those yet, but my next round of testing will include 320g CE's and 350g SMK's with RL-17. If I can run the 320's @ 2650-2700, I will have a formidable long range elk rifle. I will use the SMK's for less expensive practice to develop my skills far enough to take full advantage of the rifle's capabilities. I am also keeping a watchful eye out for the Berger .375 that is supposedly in development. I might switch to that for my practice bullet, depending on how it works out.
Though I recognize that it is nowhere near the top of the ballistic heap, I am a big fan of the ol' H&H. I am convinced that, loaded to modern levels with the latest components, the H&H has a lot more potential than people believe it does. I firmly believe that both the H&H and the 375 Ruger have the ability to punch well above their weight class (or case capacity) when fed the right powders and bullets.
I am glad to know that there are others thinking along similar lines. I am very interested in your H&H build and I look forward to reading more as your build progresses.