I have been pondering "long range" use of the h&h for awhile myself.
I got rid of my .338 awhile ago, in part because there is so much overlap between the two out to about 400 yards. Frankly, my skills haven´t progressed to the point that I can use the superior long range qualities of the .338´s. As a bridge, I am looking to develop proficiency with my .375 out to about 600 yards. That appears to me to be the practical limit of the h&h case with the bullets currently available.
I must stress that I am still in the research phase of the idea. Based on some previous discussions on this forum, I plan to start by handloading with the Barnes 250g TTSX. If it does well in my rifle and performs well on game, I will stay with that load. If not, the 260g Accubond looks like a good alternative. I figure that I should be able to push either bullet to around 2900ish plus or minus a little bit. Having run the basic numbers on the JBM ballistics website, on paper that level of performance would appear to give reasonable performance to 600ish yards.
I plan to start the initial load work this fall, but I don´t think my schedule will allow enough range work to reach any useful conclusions until next fall. Will post my results when I have something worthwhile to share.
If anyone else beats me to the punch on this, I would be most interested in the results.