I've got to say it seems very unlikely that any unit was fully equipped with a modern repeating rifle as early as April 1862, at least not as far as Regimental establishment is concerned.
For a start, I don't think any of the accounts I've read mention such a unit being present and it would surely be a noteworthy point that the various historians and authors would have dug-out from the archives.
What was the scale of the game you mentioned? If that game oob did get it's fact correct then it makes all the others wrong kinda thing ...so it makes me think that SPI "Bloody April" got it wrong.
Great reading here:
http://www.rarewinchesters.com/index.shtmlHistory of the Henry repeaters:
http://www.rarewinchesters.com/articles ... n_00.shtml...and their use in the ACW:
http://www.rarewinchesters.com/articles ... n_02.shtml...distribution & usage:
http://www.rarewinchesters.com/articles ... n_07.shtmlFrustratingly, the list of ACW battles where Henry repeaters were used is qualified by a question mark in the case of Shiloh. If there was such a unit present at Shiloh ...it's a well kept secret.