PJR's are done lying down (shoulders stay on the bench, it's not a lat pullover after all) and due the the upper arms not being perpendicular to the floor and the force being applied differently (if you were standing, think of the DB being pulled back rather than down), they really shouldn't hurt.
FWIW I had some discomfort doing the standing extensions, but that only happens when I go too heavy or my elbows are beat up from other shit... Or if I haven't warmed them up with other exercises first.
So, the actual PJR's are imo your best bet.
The standing extensions I do with a different grip though... Hands gripping the handle, not the "plate" as the latter gives me wrist discomfort etc (small hands).
Regular dips kill my shoulders too... And if I go heavy on pressing exercises all the time or use too much ROM or some such, my bicep tendons at the shoulder tend to give me trouble (no matter what setup)...
What part of your shoulders hurts? One of the rotator cuff muscles, bicep tendon, front or back...?
About the ROM... Yeah... In training, use whatever ROM gives you no pain and still gets the job done (sometimes that gets the job done a lot better than full ROM, esp. on iso stuff or if you press frequently, for example, and aren't really built for it).
Need some more info on how and where exactly you are hurting, joint by joint, and what the pain feels like (dull and spread out, sharp and localized?).
You don't necessarily need to do extensions as previously mentioned, but on most presses the medial and lateral head of the triceps do most of the work...
You could try doing wide-reverse grip benches (bar goes through the crease the flesh of your hand makes, don't use a death grip with all fingers, it's mostly thumb and index finger and maybe one other wrapped around the bar) in a non-counterweighted smith machine (straight works best imo, but if you have an angled one, set up so that as you press up, the weight also travels towards your feet)... Set up as if benching, press towards your feet as well as up (i.e. against the smith rails)... If reverse grip is too awkward for you (use wrist wraps!), then try a regular, closer grip (shoulder width or whatever fits)... Won't be able to tuck the elbows as much though.
Lots of other exercises available, but do see if you can pinpoint what causes your elbow pain and try to fix it...
Not sure about your shoulder pain etc, give more info on where it hurts and so on.
Bushidobadboy and some other posters are very knowledgeable when it comes to such things, try shooting him a PM (don't think he reads the PL forum, but I'm not sure) or post in the injury forum.
Where do you feel a click when doing extensions/CGP? Shoulders? Elbows?