The 1860 drop-in cylinder should fit the Pietta '51/44 as the gun is basically a 60 Army with Navy gripframes and a 44 bored Navy style barrel.
However, most I have seen were brass framed revolvers, and the brass frame should not be converted.
If yours has a steel frame, the 60 Army cylinder should work. Some tuning will probably be required, as the R&D 5 shot cylinder overtravels in many guns, and the handspring tension and the bolt spring may need to be adjusted.
The 44 cylinder cannot be mounted on a 36 Navy frame because the Army cylinder requires a rebate step cut in the frame for the enlarged forward portion of the cylinder, as seen on the 1860 Army. The barrel extension is also different, as the Army cylinder is longer than the Navy, so a 36 caliber Navy barrel cannot be mounted on an 1860 Army frame with the Army cylinder installed.
So there is no need to worry about any "genius" doing that. However, that mistake is easily done with the 58 Remington 36.
The opposite is possible, however, an 1851/61 cylinder and barrel can be mounted on an 1860 Army frame.