Replacing the 5/3/1 piecewise
I also did Wendler's 5/3/1 for a while, and ran into the same problem. Obviously there is no one-size-fits-all solution to questions like these, but I do recommend switching programs that aren't working out. The good thing about 5/3/1 is that it lends it self to piecewise substitutions. You take nothing away from the other days if you just replace the OHP part, and vice versa.
Personally, I kept doing 5/3/1 for other exercises, but for OHP, I went a separate route, and found a different shoulder day program written by Jeff Cavaliere. I'll copy/paste the program itself here, and link the source so you can see the full walkthrough with explanations of caveats.
OHP or Handstand pushups - 4 sets of 12,8,6,6 reps
Finish with one set of dumbbell and band overhead presses for neuromuscular re-education x 15 reps
Delt Stretch Tri-Set (21’s) - 2-3 sets of 7 reps in each direction for rear, middle and front delts
Make sure you perform these in the order of rear to front to account for fatigue.
DB Cheat Laterals - 3 sets to failure on each arm
Immediately into a DB Push Press to failure on each arm
Cable or Banded Face Pulls - 3 sets of 15
Perform these with a mindset of 15 sets of 1 to ensure highest quality of every rep.
In the video you will find that he pinpoints exactly how and why each exercise is done, with anatomical explanations as to how you ensure each head of the deltoid is hit.
The gist of what makes a good program
In order to achieve progress, we need to make sure that we overload the muscle in all the different ways. Weight is one component, which is why we do the OHP in the first place. The other, auxiliary exercises that target more specific subsections of the shoulder, allow us to achieve metabolic overload (repping until it burns... and then some!).
By doing these smaller exercises, you can always adjust the weight for that particular muscle, instead of having to go with a low weight because one muscle is weak, taking away from the potential progress of another muscle that could handle more.
This is also why bench press is a good chest exercise (allowing lots of weight), but not a silver bullet (lacking the ability to target different parts of the pectoral, and not allowing transverse contractions).