2012 Prius - Mysterious Driver-Side "Clunk

Hey everyone,
I’m chasing down a frustrating clunking sound on my 2012 Prius and could really use some expert eyes on this.
The Symptom:
I am getting a distinct, back-and-forth "clunk" or "knock" from the driver's side of the engine bay. It isn't a continuous rattle—it's usually just 1 or 2 random clunks that happen right at the exact split-second the gas engine cycles on while the car is idling/stopped. To my ears, it sounds like it is coming directly from the rear transmission mount area.
What I’ve Already Replaced/Done:

Main Transmission Mount (Driver Side, behind inverter): Replaced yesterday.

Rear Transmission Mount: Brand new. Replaced 2 weeks ago

Lower Torque Strut Mount: Inspected, rubber looks solid with no cracks.

EGR System & Intake Manifold: Completely torn down and cleaned out recently to clear all passages.

Sway Bar End Links: Checked and verified tight.

Because it's a transient thud right when the engine catches, I thought it might be a bad passenger side engine mount, since it's the only one I haven't checked, I did a visual inspect on it and it doesn't appear to be collapsed.
Given that the driver-side and rear mounts are brand new and torqued down, what could be causing a localized clunk near the rear mount just as the engine kicks over?
Could a weak passenger mount still cause enough pivot/leverage to twist the drivetrain and slam against the new rear mount? Or should I be looking into subframe/exhaust clearance, loose bracket bolts, or something internal like the flywheel damper assembly?
Appreciate any insights or similar experiences!

 

62k miles