I don't want to put you off on this project but IMHO, it's a lot of work, which I know you are capable of doing.
Still, in the end, it just may be cheaper to purchase a rifle in that chambering, which is excellent and I fully understand your interest.
In the past, I have converted a few to 300WM and even though the rifles turned out to be presentable as well as accurate, they were still valued at less than the cost of a new barrel, which I was luckily able to avoid.
For the 375H&H You can easily open up the bolt face but that will be the least of your issues.
You're going to have to come up with appx a half inch of extra length in the mag well as well as bolt travel.
The mag well will need to be enlarged at both ends and the receiver will need some alteration to open up the magwell opening as well as reshaping the rails.
It would likely be easier to do a build on a P14 action but not much.
IMHO, this is a very hands on, work heavy, time consuming project you are considering.
Then of course there is also the cost of making up a new stock to fit this rifle. ETC ETC.