Hi, General,
Here is an interesting web page on all the rigamarole that goes into firing an artillery round:
https://www.civilwaracademy.com/civil-war-artilleryChecking Jack Coggins' Arms and Equipment of the Civil War, the diagram shows the limber 20+ yards to the rear of the gun muzzle, according to regulations.
I'm thinking the most efficient way to clear the gun is fire off what's loaded and hope your supporting infantry does their job while you prepare to load and fire a more appropriate round.
I read Long Arm of Lee but I don't think it was specific enough to cover situations like the one you outlined.
Here is a well-regarded book I haven't read though:
https://www.amazon.com/Grape-Canister-L ... 0811707024Late thought: I know they fired double canister. Wonder if it was possible to load canister on top of a different round?