It appears that others agree with your opinion about using a 44 magnum case to duplicate the original loading. I am not certain how it is fired since the original cartridge was a rimfire and the modern 44 Magnum is a centerfire boxer primer. I would not like to work with the sensitive chemicals required for a rimfire ignition system. You would need to clean the old primer out and then replace it with new. I believe that centrifugal force is used to do that at rimfire factories. As a reloader and a person who has worked in chemical laboratories, I consider repriming rimfires as a potential risky business, not so much the priming as the preparation of sensitive enough unstable compound suitable as a primer.

The Henry 44 rimfire used usually a 200 grain lead bullett at .446 diameter with 26 to 28 grains black powder at approximate 1125 ft/sec and 568 ft/lbs energy.

Reproduction Henrys are usually chambered for the .44-40 round.