Order this exhaust "insulator" from Amazon.
Walker Exhaust 35259 Hardware-Insulator : Amazon.com : Automotive
Install it where the Nismo muffler hanger is just hanging. That should fix it. I installed a used Nismo exhaust on my base a few weeks ago. Knew about the difference ahead of time so I had this ready. Used the metal insert and bolt from the base insulator, so if the shop trashed it, you will need to source those. Since this one is about twice as long as the shorter one from the base muffler, it worked out perfect.