Well, my problem is likely completely different from yours, and unfortunately I have no expertise at all regarding how people with various shoulder problems should train.
The exercises that I have found I can do without aggravating things are:
Smith Overhead Press, with some recline to the seat.
Front Delt Plate Raise
Machine Lateral Raise but only with light weight
Machine Rear Delt Fly
Chest pressing is also restricted but I can do barbell Incline Presses and Smith CGBP’s, as well as Hammer Strength Flat Bench and Seated Incline.
By the way, on the Smith machine, if you can unclip the cables that provide the counterweighting, this ENORMOUSLY improves a Smith machine. It also substantially changes the weight that you add to the bar. I am sure the machine I use employs at least 40 lb of counterweighting. With the cables in place, the empty bar provides only about 25 lb of resistance or less. Without the cables, the empty bar weighs at least 65 lb.
But this is not the important part: the important thing is that the thing is transformed into feeling alive in your hands and very quick-responding. I think you will find that for those specific exercises where the path is suitable, once the counterweighting is removed all objections to the Smith machine will disappear.
Anyway, yesterday’s shoulder workout was:
Smith Overhead Press. Turnaround point about 1 or 1.5 inches under the chin.
Starting with 60 seconds rest. 115/5, 135/4, 155/3, 165/2. Changing to 90 s rest: 175/2, 185/2, 190/2. Now 2 min rest: 195/2, 200/2. Then 3 min rest: 205/2. Felt done here. Last rep might have been slower than CT would like but is IMO suitable for me. Could have gotten a third rep but it would have been virtually or actually maximal.
Top Overhead Press, as in video
60 seconds rest: 115/5, 155/4, 175/3, 195/3, 205/3. 90 seconds rest: 215/3, 220/2, 225/2. Two min rest: 230/2, 235/2. Three min rest: 240/2, 245/3.
Incline Press. Slightly higher than normal incline. Turnaround point a few inches above the chest due to ROM. Still following CT’s rep method, except on the final set the extra reps were more “push them out” than focusing on explosiveness.
215/5, two min rest, 195/5. Then on 1 min rest, 175/4x5 and a final set of 10 reps that really surprised me.
The last was not a Thibaudeau protocol so far as I know, but the “Bear” protocol described by Pavel Tsatsouline. I wanted to finish off with some volume at more moderate percent 1RM. Though using the approximately-correct weight drops – 10% of the starting weight – I used too little weight, but that’s OK. The general method though is to be able to get no more than 5x5 at the brief-rest lightest weight and it’s perfectly acceptable to get only 3 or 4 sets of 5 and end there.
The reason for giving weights instead of percentages is I thought it would be easier to read. Besides, that saved the trouble of calculating them, and it makes clear that the weight jumps are simple rather than some highly precise calculated values.
Roughly speaking my planning was to use triples for midrange weights but switch to doubles on reaching about 80% 1RM, and when quite light do 4 or 5 reps if I wanted to, though triples would have been fine there instead. Part of the reason for doing for example the 5 reps at 115 lb was that after doing the third I felt there was still room for improving the explosiveness within the set.
All this worked the shoulders pretty thoroughly (not rear delts though but that was according to plan) and caused me no aggravation that I can tell.
But it’s possible it could be horribly inappropriate for you. Hopefully not, or at least hopefully there are some very effective exercises for you that will be acceptable for your shoulder.