Passenger Door Buzzes with Engine Idle

When the car runs at a certain RPM during idle, the door panel rattles/buzzes.
This is usually when the car is first started. The idle speed changes at some point as it warms up and then it no longer rattles. Sometimes it also buzzes during acceleration when the engine hits a certain RPM or when driving on coarse spots in the road.
It has been very difficult to reproduce it at the dealership because there seems to be no way to control when the engine runs and to control the RPM. On top of that, it is affected by ambient temperature. If it is isn't cold enough, it doesn't happen.
Is there any way to manually control starting and revving the engine?
Is there any well-known issue that causes this or a known fix for the buzzing?

 

I haven't tried to reproduce it on purpose while driving, but that sounds about right. It is most noticeable when the engine kicks in to warm up on a cold day when I am backing out of the driveway or a parking space.
It is a 2010. It seems related to the door because I can stop the noise by opening the passenger door. When I close the door it comes back until the engine RPM automatically changes.

 

In case that's it, what other fix is there for that?

 

I was able to get that very specific buzz described above fixed at the dealer after they applied the TSB last week. It took 2 days for then to send the car to a glass/body shop to do the work. Everything seemed fine when I picked up the car so I thought everything was finally fixed, but when the car was started the next morning there was still more buzzing noise than ever.
Now it sounds like the entire dashboard instead of just the passenger door panel is vibrating when the car starts for the first time in the morning. It's even louder buzzing vibration noise than before.
If I drive the car and restart it later, the car idles differently and doesn't trigger the buzzing.
There is something unique about the way the car idles to warm up the engine the first time the car is started vs the way it idles when the engine runs to replenish the battery charge later. If I were to drive the car to the dealership and try restarting the already warmed up car, I would not be able to show them the issue.
Because of this, the only way I would be able to replicate this problem would be to drop off the car at the dealership overnight and make sure that they have the technician who is going to work on the car personally start it in the morning before the sun heats up the interior instead of having a porter pick up the car and bring it to the technician.
Has anyone seen this dashboard buzzing on engine warm up before? Is there another TSB for this?

I'm getting really tired of this now. On one hand, I'm glad plastic buzzing rattling and squeaking is the biggest issue I had with the car versus some serious mechanical failure, but it makes me hate driving the car.

If they cannot fix this, I will get rid of the car and never buy another Toyota again. I would rather have easy to replicate and fix problems than chase phantom rattles constantly.

There is also a newer rattle in the rear hatch back area that make noise when the car hits every bump in the road. Reminds me of the kind of rattles would hear riding around town in an old taxi with 300K miles on it. Since this rear rattling behind the seat didn't start until after the warranty expired, I won't be able to get Toyota to cover it under warranty. I may just live with that one since it is a less annoying sound.
The front dash/door rattling has been a problem for at least the last year and was attempted to be fixed twice under warranty and was never fully resolved.

 

I just thought of something that might be a simple fix. I remember having a Honda that had a squeaking moonroof and it was fixed by putting some kind of lubricant on the seals around the roof opening.
Since the buzzing sound I hear in the Prius goes away when I open the passenger door, I wonder if it could be something similar?
Is there some kind of grease or lubricant that is recommended to be applied on the door seals?
I could try that and see if it makes this buzzing go away.