Noise coming from dashboard rattle

VIN 4T1BF28B2YU022042.

The problem started about a year ago.
It took some time and experiments to locate the trouble place.
A rattle noise started coming from the top plate/bar on the dashboard.
This plate/bar is made from a soft flexible material.
Under that plate/bar goes a thin black plastic tray, snap connected to that top plate/bar.

The noise never comes on when the car is moving.

The rattle noise is coming on only when the car is on idle
(the engine running, the gear engaged, but the car is not moving - typical for
stopping on red light, parking, etc.).

Trying to eliminate this noise, I noticed:
A) Turning off the blower motor helps for a short time,
then the noise comes back again.
B) Turning A/C off or on does not affect the noise.
C) Disconnecting and removing the plastic tray from the top bar/plate did not help.
D) After disconnecting the plastic tray, putting shims under the bar/plate did not help.
E) The only thing that helped was this: with the plastic tray originally snap-connected to the top bar/plate, pressing them to each other in two points, 3" right and left from the center, with a heavy-duty 2" spring clamps helped to almost eliminate the noise. It was clumsy, but it worked. That gave me a (crazy?) Idea of drilling at those points for putting screws, that will press those two pieces to each other using nuts, smaller and larger washers (steel and rubber). I did not do that yet.
I understand, that if I do I will need a Right Angle Drill.
Note:
Motor mounts, suspension, steering system are recently renewed.

Please suggest on how to fix my problem without going to the dealer.
Albert