Q: Rattling sound after rebuilt head. Solid CEL. Car begins to rattle after 3-4mins warmed up and begins running rough

Hello I recently just overheated my 1.8t and had the head rebuilt. Replaced all worn out hoses and sensors. The car upon first start up made an off rattling and shaking as if it was misfiring. If I let it sit and start up the car will purr and runs as normal for a few mins until you hear a sensor shut off (SAI?) and the idle then drops to 800rpms from 1,100 and begins to make the rattling noise. The rattle either appears to drown out above 1,100 rpms or is gone when revving the motor. After a few mins of of this the car began to hesitate somewhat in the lower rpms range almost as if stuttering.

My car has 150135 miles.
My car has an automatic transmission.