Lee knows of this drawing of bullet to smaller sizes using their 7/8x14 threaded cast bullet sizing dies.

With their dies, for drawing .375's to .366", they suggest a 3-die set, as well, from .338" down to .330" for the .318 Rigby or the 8x56R.

As well, 8mm bullets can be drawn to .312 to .315" for various .303's.

I think they might charge $30.00 each for these dies, which come with the appropriately sized rams.

A phone call to Lee will hopefully elicit a positive result for you. Note, that the final draw die should be .365" as there will be just about .001" spring-back.

Just some of the .375" bullets I was playing with. In the bottom picture is the die I cobbled up out of a Pacific .222 FL die. I tried this with .223 RCBS dies and it didn't work. In the bottom picture on the right, are the 200gr. Sierra FN and the .220 Hornady FN.
Top picture:
220 Hornady FN
225gr. Hornady SP
235gr. Speer SRN
300gr. Hornady RN Interlock
300gr. Hornady RN Interbond

All of these bullets shot MOA or slightly less for 3-shot groups.