The only difference between the R&D cylinder for the Pietta and the Uberti is the backplate, which is thicker for the Pietta. There used to be a bolt slot difference, as the Pietta used to be thinner, as I recall, but I think they're the same now. I have an older Uberti which has the longer cylinder Uberti used to use, and it is fitted with an Uberti cylinder and a Pietta backplate. A Pietta cylinder assembly fits it, however.
I have to be careful not to shoot that older Uberti when using the newer ones as well due to the cylinder length, and use it with the Piettas instead.
I just measured them to make sure of my memory. Both the Pietta and the Uberti cylinder are 1.62 long, or a bit over, but not 1.625. I'm not sure why they are stamped U or P, unless there is some other subtle difference R&D has in their machining.
The Pietta backplate is .395 thick, the Uberti backplate is .380 thick. If you can get an Uberti backplate, which is your best option if you intend to have more than one, your cylinder will work in the Uberti revolver. They are also stamped either U or P.
Kirst has the opposite situation, the Kirst backplates are the same, the cylinders are different lengths.