I can't address your specific question since I am not familiar with the Plainsman rifle. However, many years ago I replaced the original percussion lock (without a bridle) on a CVA Kentucky rifle with newer CVA lock that did have a bridle, as well as a fly in the tumbler. The lock plates were the same size and the newer lock fit the existing mortice perfectly. The rear lock bolt had to be moved about 3/16" aft if I recall correctly. An oversize lock bolt escutcheon hid the abandoned original hole.
The lock from a CVA Mountain Rifle might be the same size as the early, no-bridle locks but I am not sure.
Hopefully this info is of some benefit to you in your quest. Good luck.