I’d say start doing some olympic lifts, just to get your body working as a whole chain, instead of just using shoulders and arms, power cleans really seemed to do wonders for my shot. They also help with explosiveness.
You’re right, upper body strength does play a significant role in the shot put, moreso than the discus, javalin or hammer. Instead of picking pushdowns, laterals and other assorted isolation movements, I would center your upperbody work around Jerks, Pushpresses and DB Military work.
That was for the upper body. The lower body is more important in generating power for the throw.
I would agree w/ jeff good call on adding lower body work. Also abdominal strength especially obliques are important to train. Do a lot of twisting motion w/ cables, single dumbbell twist w/ phisoball etc…
Push-press and Power Snatch. The snatches will hit the abs/obliques. Also, you might want to try these with dumbells, since the shot put is unilateral (correct me if I’m wrong, guys).