You could get a 3-die set to reduce Sierra 200gr. FP .375's, down to .366".
These cast bullet sizing dies for this purpose are not on their web site.
They have to be ordered peace meal. Lee is aware some people are doing this so this makes it easier.

I made a single die to do this out of a .222 Rem. Pacific sizing die and my throating reamer for .375. It works perfectly. I tried to make another out of RCBS .222 Rem. dies for a fellow and it was not very successful. The one made on the sizer die failed, but the one on the seating die worked after a fashion. I do not remember why this was, perhaps die hardness or some other reason? I did not have to anneal the Pacific die, but did with the RCBS dies.