I do everything except operate the handle with my left hand. I pretty much never let go of the handle with my right hand.

Two tips I can suggest that work well for me.

1) I put a 5 gallon bucket under my press to catch any primers that don't dispense properly first try. I set mine on top of an overturned milk crate - that is what I found would put the top of the bucket about a foot below the ram when it is in it's lowered position.
2) I dispense the primers in a two step motion. Swing it into position with my left thumb against the bottom of the angled face of the dispenser head and then once it is in place I kind of "roll" my thumb up the angled face of the dispenser head to push it forward and down to dispense the primer.

That's what works for me, but as with all things reloading, YMMV...