Your Palmetto {iron mounted "spiral tree"} is 100% correct, as far as the photos' you posted. PM me if you need more info.
Your Palmetto should be rifled {3 broad L&G}. It is probably a Happoldt alteration on an original 1852 pattern Palmetto. He also altered Palmetto rifles and some 1841 model "mississippi" rifles for the state at the start of the War. William Glaze also rifled and sighted 3720 of the brass mounted muskets in 1861.
To replace the original 1852 block rear sights, when rifling the guns, Wm. Glaze and John Happoldt {the contractors in 1861} apparently used different type rear, long range sights, but there are not enough of these guns in collections to make aany definitive conclusion as to who did the alteration. They used whatever they had to complete their contract. Confederate made and altered guns, with the exception of a few major armories, were not even close to the standards of US models. Most of the paperwork in Columbia SC was rather charred during the War.
The Glaze alteration, done in 1861, consisted of general repairs and clean up plus rifling the barrel {3 grooves}, cutting a dovetail and adding a rear sight, but rather than the simple block "V" sight he added the long range sight which is still on yours. As these muskets were taken from storage, his alterations could be on both the "bushy" and the "spiral' locked guns.
All Palmetto products; muskets, rifles, bayonets, cutlasses, etc are very collectable and rarely found with any "condition" remaining
Here's some photos of the "other one".
A brass mounted "bushy" tree:
The rear sight (the sight stamping guy hade some problems with the "2"} Love CS stuff !!!
With the new rifling you'd "need" that 700 yard + ladder...
The brass mounted guns mostly had top bayonet lugs, but top or bottom were somewhat varied depending on the bayonets on hand at the time of alteration.