This post caught my eye. My mind jumped to SHOULDERS!
I have loose shoulder joints - seen doctor - nothing major just my body.
Thing is I'm right-handed but my right shoulder is the weakest (loose joint).
I notice this 'looseness' in my shoulder joint affecting my lifts on pressing movements.
My left pec is slightly bigger like you.
In fact in all pressing movements my left non-dominant side is stronger.
I'm the only one who notices it. You're probably the only person who notices yourself as well. Its just not possible for either side of the human body to get too much out of sync with the other.
There is very little you can really do to solve the problem other then just ...wait for it... strength training!
If it is shoulder instability which is your problem then I reconmend dips as another chest exercise in addition to bench press to build chest and tricep strength. This will carry over onto your bench. And a bigger bench means bigger pecs! Too easy.
On barbell bench lifts you might not notice one side doing more work. Use dumbbells and you'll see one shoulder failing much easier.
Dumbbells will also force you to stablise your shoulder joints more than a barbell and this is what you need to do.
So in summary do these exercises (in order of importantance):
You could also through in some pure shoulder work. A doctor got me to try some exercises with resistance bands. Didnt do anything for me. My opinion is heavy pressing will ultimately strengthen my shoulders and fix any imbalances.