Boyds offers walnut stocks and has some grade upgrades IIRC. They offer laser checkering too, but it looks kind of dark to me. You may like it. The base prices are good, but extras add up pretty quick. With a .375 you're gonna want crossbolts and glass at stress points I would think, another reason to consider fiberglass.
Is the original hopeless? Whitworths were pretty nice right out of the box as I recall.
Actually, the stock that came on it is laminate with crossbolts and glass. It's kind of interesting as I've never seen a Whitworth with this stock before. All I've seen have the Zastava walnut.
I just don't know enough about the Interarms that were finished in England to know what stocks they put on them.