Cummins NHC 250 with dead cylinder...need some experts on the old engines

I don't think they use the oil spray on the piston on a 250

 

Since the failure was limited to one cylinder it is more likely to be an injector problem especially since you stated at first that it had a slight miss. Cam follower timing never changes and it would effect both cylinders. The other rare instance was that one time we Cummins mechanics felt that if you adjusted an injector tighter that it would advanced the timing. (yes) I know rare thought. Never worked out, only made a low power complaint after it messed up the injectors. Finally there isn't piston cooling jets on the 250. That came in with the 290's. If you adjust the injectors you have two methods but the easiest and it runs OK with in the torque method.