OK, that makes sense. I don't want to cut into the 3" stack and replace the 3"x3"x2"x1 1/2" Tee (see attached pic) that is there because I'm not sure I have the space to do it, even if I use a 3" banded coupler.
So my next idea is to run my new 2" drain past the big Tee and "Y" into the 2"...