I have a 04 rx8 (obviously ). I read some Forum's and if mine is doing the same as there's it's the motor mounts. https://www.youtube.com/watch?v=4Z0lXcdQrVE
hopefully link will take you to my youtube video....... any help will be much appreciated

 

I can't give you any advice sorry, but it is funny, how it dance

hope you find the way out, and solve the problem