Brendan, you have to focus on what they call the posterior chain = scapula stabilisers, posterior rotator cuff, thoracic extension, gluteal activation plus rotational movements.

This can all be enhanced by a more open and expanded postural orientation adopted during all exercises.

Likewise the core stabilisers and rotators of the mid section are very important to contribute to shoulder function.

Further, flexibility around the pelvis, lumbar and thoracic spine is very important.

Notice I haven't mentioned the powerful adductors = pec major, lats dorsi

These muscles are important to functional movement but should not be dominant contributors to shoulder stability. They are torque producers not stabilisers.

So exercises I recommend
  1. External rotation through Abduction against a very light load (combined with an active lower body posture like a throwing position to activate gluts etc)
  2. Lunges +/- external rotation
  3. Deadlifts (very technical so take it easy)
  4. Core stability exercises with a swiss ball
  5. Thoracic extension back over a swiss ball
  6. Hanging Pull Ups
  7. Biceps and Triceps
  8. Crawling out to a plank (hold) and crawl back up into a standing position
  9. Burp Pees
To get a visual idea of what I would recommend in a gym program take a look at my website Shoulder TV | Shoulder Guy Physiotherapy Pty Ltd

Overall the focus needs to be on those muscles that contribute to stability.

The exercise list is not exhaustive and is general advice only.

Cheers

Luke