Not a popular tip -- but you may have to switch to a more "neutral" or "supinated" grip style of pull-ups (often called "chin-ups") instead!!
This is because the lats, in addition to being shoulder extensors, are also strong internal rotators of the arm (an effect which may be even further enhanced due to them also overlapping the inferior angle of the scapula as well). And, in individuals with certain shoulder anatomies, applying forces across internally-rotated shoulders can lead to shoulder issues --- instability, impingement, pain, etc... -- to the extent that the body may well subconsciously "restrict" and significantly limit the forces provided by the lats just to protect and prevent injury to the shoulder complex! Consequently, as a result, your "other pull-up muscles" -- i.e., elbow flexors such as the biceps, brachialis, brachioradialis -- will then have to "pick up the slack", and you may end up feeling like the whole pull-up exercise ended up just being a workout for your arms!
And so to get around this, you may just have to start doing pull-ups with a more externally-rotated (aka "neutral/supinated") grip instead.
** Edit -- interestingly enough, using a "pronated" grip is often said to actually target the lats more relative to "neutral/supinated" grips, which are sometimes said to instead target more the biceps and/or the brachialis. But, if you're an individual with the suspect shoulder anatomy described above, your body may limit the recruitment of the lats and thus as a result your "pronated" pull-ups may end up mostly targeting the brachioradialis forearm flexor instead! So, rather than a "lats workout", those pronated pullups may simply end up being just a "forearm workout" instead!
** Edit #2 -- in fact, perhaps ring pullups may be the ideal pull-ups variant here! Notice how the hands externally rotate during the concentric phase of the exercise -- this should help "counteract" the tendency of the lats to internally rotate the arm, and consequently enforce a safer and more comfortable "trajectory" of the arm and shoulder complex for the exercise!