I had a couple of original .32-44 Target cartridges to display with the revolver I had years ago. As I remember they weren't actually wadcutters but were regular round nose or round ball that were seated completely within the cylinder length case. (kind of like the gas-seal Nagants.)

Jinks & Neal and SCSW3 both show that the regular NM#3 also had some chambered in .32-44 in addition to the Target Model. A letter would definitely be in order if you end up with it.

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Dean
SWCA #680 SWHF #446