Tom is right of course. The 45 Schofield case was actually much-used by the US Army in the west due to its being able to fit either of their issued revolvers, the Schofield or the SAA, whereas the "Long Colt" only fit the SAA.
You will probably be better satisfied with your conversion if you go ahead and get the Long Colt cylinder. You can still use 45 Schofield cases if you so desire, but you can also use the much more popular 45 Colt cases. This is a huge advantage. Since neither was used in Remington conversions historically, there is no disadvantage either way as to period accuracy.
As to getting the cut made, it boils down to historical accuracy vs. convenience. Certainly the loading of the piece will be much easier to accomplish, but the originals did not have the loading gate.
