According to Mike Venturino in his book, "Shooting Sixguns of the Old West", the .44 Colt cartridge would not fit in the .44 Remingtons that he had. He had to use a very tight .44 Spl/Mag sizing die to get the cartridge sized small enough to fit in his original chambers.
Several years ago I had two .44/40 Remington 1875 revlvers that I converted to shoot .44 Special by having a pair of .357 Mag Cylinders bored out and fitted to my remington 1875's.
Those cylinders will shoot the .44 Russian, the .44 Colt and the .44 Special. I only shoot the .44 Colt out of them as they are the only cartridge that is close to the original .44 Remington. Wether I shoot 200 grain, 240 grain, or 215 grain bullets I seem to shoot to point of aim at CAS distances.
If I were you I'd go for the .44 Special chamber and shoot the .44 Colt brass out of them. You can duplicte the original .44 Remington loadings at your pleasure using the heavier bullets.
As a side note, the Army's Frankfort Arsenal in Philadelphia, PA made cartridges to be used in both the Colt .44 Conversions and the Remington Conversion. The cartridge that the Remington Conversions used were transfered over to the 1875 model revolvers. Have fun on whatever you decide to do.