I have a pre-64 300 H&H that I picked up for a song. I have restocked it and had it Cerakoted. I could give a damn about the value- I have a better rifle now. I am going to resist the urge to rechamber to 300 WBY for now.
Having put several thousand rounds through my 300 WBYs, let offer a couple of suggestions. 165-168 TSX or TTSX pushed by H4831 or H4831SC is all you need. It's fun to play with stuff but this has proven to be accurate and deadly in about 6 different 300 WBYs (effectively what you have). Never found a better powder for my WBYs (without freebore). That is why I suggest it. In a WBY with freebore, you might explore the slightly slower powders.
The recoil pad was almost certainly added by someone and if it is like the one on my 1952 vintage 30-06, hard as a board. You would do well to change it out to something softer. I really like the Pachmayr presentation pads. They look good and work well enough. The ultra soft ones are good to, just harder to install and make look good.
Have fun
