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I am contemplating about sending out transfer applications for Fall 2018.

Currently: T3 (NY) + Top 10%
>50% scholly, but school will bump it to full scholly for my last two years.
AA - not sure if that matters at this point.

T3 has already asked me to do OCI.

Ultimate goal = big law --> become a professor --> (also want to live in NY)

I want to apply to Georgetown and Cornell. I may throw an app at NYU, but it depends on how this semester goes.

Only problem is - I don't know if I wanna lose the connections I have at this school! But I keep wondering if the "name" will hold me back....

Any advice would be lovely!

If your goal is truly academia (and tenure-track academia not like legal writing prof), then yes the T3 will hold you back for pretty much any reasonable law school to teach at. Though, the truth of the matter is outside of HYSCC the dropoff in academic placement is significant. You'd need to be pretty high in your class at a T-14 and have some research agenda plus some other prestigious things in your background to have even a "reasonable" shot at academia if you're not at one of those. Even the people at HYSCC have a somewhat uphill battle to academia.

A career as a tenure track law prof. usually requires significant published work & graduation from a highly ranked law school with stellar credentials.

Currently, it appears that you are a student at New York Law School, or, possibly, Pace or Hofstra (with Albany Law & SUNY Buffalo being possible as well). While free tuition is attractive, it is not likely to result in biglaw followed by a law school professorship.

The better course of action is to aim for biglaw, get published & get significant experience in one practice area, then become an adjunct professor while remaining at your law firm. Whether or not top 10% is adequate to place into biglaw from your current law school is another issue, however.

No harm in applying as a transfer to Georgetown, Cornell, Penn, NYU & Columbia.