The following is meant as friendly, educational information -- not argumentation. Pardon me, please, if you already know all the info.
The USS Monacacy's artillery armament list incudes a "20-pounder" Dahlgren Rifle. That cannon's caliber is 4.0-inches. So, if your larger Schenkl shell is 4.5"-caliber, it cannot have been fired the the Monacacy.
As I mentioned previously, a 4.5"-caliber Schenkl was for the the US Army's 4.5" Siege-&-Garrison Rifle, a Land Service cannon. Also as mentioned previously, it was so ponderously heavy that it was used in very few civil war battles. I have to say, as it was such a ponderous cannon, so seldom used, it seems not very likely that any would have been sent on the Korea expedition.
That being said, there was a 4.4"-caliber Schenkl shell. It was made for use in the US Navy's 4.4" Dahlgren "30-pounder" Rifle. (The USS Monacacy's "20-pounder" Dahlgren Rifles were 4.0-inch caliber.)
You see why we need truly Precision measuring of your shell's diameter to help you accurately determine which ship (or battery) fired it. Of course, with uncleaned excavated projectiles, any rust/dirt-crust thickness must be carefully accounted for and excluded from the diameter measurement.
In case you don't already know... projectiles for Muzzleloader cannons were always a bit smaller in diameter than the cannon's bore. For example, a 4.4"-caliber Schenkl shell's diameter was typically about 4.35 inches.
Sidenote:
Civil war artillery scholars have urged people to use a "pounder" designation only for Smoothbore cannons. With Rifled cannons, the "pounder" designation tends to cause unnecessary confusion. Here are some of many examples:
"12-pounder" Dahlgren Rifle = 3.4" caliber
"12-pounder" Blakely Rifle = 3.5" caliber
"20-pounder" Parrott Rifle = 3.67" caliber
"20-pounder" Dahlgren Rifle = 4.0" caliber
"30-pounder" Parrott Rifle = 4.2" caliber
"30-pounder" Dahlgren Rifle = 4.4" caliber
Regards,
Pete