I found some info which maybe help,though doesn't tick all the boxes.your little mexican war howitzer could be a sample from foundry in pursuit of supply contract.Following info comes from....David A Norris 'American's Civil War' of Sep.1995. is about Mountain Howitzers first delivered to US Army in 1837 ordnance manuals refer to them as Model 1841.Were used in Mexican War and Indian Wars. Main manufacturers were....
Cyrus Alger & co. of Boston and James T Ames of Chicopee both of Mass.
The bore was 4.62 which fits well but barrel length was 38 inch which doesn't.If you can have a sniff around these two manufacturers, maybe hit pay dirt..........or curse Scotsman.all depends on how curious you are