Can you post a video of the noise?

 

Don't know about the rumbling you mention so its a bit of a long shot, but you might check your SAI tubes at the corrugated part. I had a noise that sounded like what you're describing, it ended up being a small tear in the SAI tube that was leaking in tune with that cylinder. It was in the curved part facing toward the engine so it took a while for me to find it.

 

I finally replaced the center bearing and the noise went away. Thank you!