No. D models are the same DA as the DA/SA guns. The D spring is often installed in DA/SA guns as an upgrade. You are correct that the “jostle” you are feeling is over travel. Luckily, that’s not an issue on all Berettas.
The other trigger action you are thinking of was the “C” variant of the PX4. It was Beretta‘s answer to things like “reduced DAO” options like the HK LEM and the SIG DAK. Beretta only offered the C variants via agency sales. A few have popped up on the market as agency trade-in guns, but they are actually kind of rare.
https://www.gunsamerica.com/digest/t...y-at-its-best/