K,,two things.
First off,that warm up can make a HUGE difference,,,just a few stretchs across the chest with each arm an a few like your trying to scratch your back by reaching over the off side shoulder,,,,for me they stop the type of ache your talking about in it's tracks.
The other thing is shooting relaxed.
Don't try to mussle anything,,your best power will always come from a relaxed beginning.
I have damage in both my shoulders,,thankfully not rotator cup,just tendon an mussle which can be managed quite easy the way I've described.
good luck.