How to switch from merchant banking at a bulge bracket to investment banking?

I'm currently working at a bulge bracket bank in New York in their merchant banking division doing tax equity project finance (think JPM / BAML). I have been exposed to a lot of modeling but more on a project scale rather than a company scale. I believe our models are more complex than banking models because of the nature of back-leveraged finance projects but I want to do more advisory / m&a on a company scale.

I'm not sure how to proceed to switch to investment banking.

My first thought was to work very hard and receive a return offer in my group and try to leverage that to switch into investment banking but I'm concerned that this is looked down upon and my full-time offer chances might be hurt if I try to switch. Also, how exactly do I go about switching? When should I bring it up? Who do I bring it up to?

My other idea was the apply to other BB and boutiques in their investment banking division. My concern here was twofold. Firstly, I've heard that the banks talk to each other and I'm worried that if another bank sees my resume and talks to my group, it will hurt my relationship at my current group. Secondly, how do other banks view my application from SA to full-time before my internship has even ended? Does being in merchant banking hurt my chances vs other IB summers?

Any advice would be greatly appreciated