2006 MDX Transmission fit in an 2004 MDX

As the original owner of a 2004 MDX, the radiator failed, was replaced by the dealer and after 3 months there is a howling noise from the transmission under load. Example: Sitting on level ground, placed in Drive, brake is on, and the howling noise starts.

I am under the impression the torque converter has failed and a replacement transmission is needed. Since the 2004 has 167K, I am searching for a used low mileage transmission from a 2005 or 2006 MDX, but I'd like to confirm a direct fit replacement for the 2004.

Is the 2005 or 2006 MDX transmission a direct replacement option for the 2004 transmission?

Thanks for your help.

Paul C.