What FD are you using? When you say “…they drop chains more often…” it implies that you had drop chains before, on round rings, now you’re seeing more. Am I right?
Right now, with round rings, I am careful with front shifts (I make sure to unload the crank arm and then gently pedal over as I move up to the big ring, that’s how I thought everyone does it). Is this what you meant by being careful?