Get some .38-55 brass and trim a bit?...
http://www.midwayusa.com/product/249870/winchester-reloading-brass-38-55-wcf-bag-of-50
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Actual .375 is about ten bucks more and only available as a seasonal run. I don't believe (IDK) Win or Starline would bother producing caliber specific weaker brass.
Anybody on here have a gun in this caliber or know someone that does?