FT Recruiting from a Semi-Target with a SA offer at a no-name balance sheet bank

Hello everyone, 

I'm currently a junior at a semi-target on the West Coast. For the last recruiting cycle, because of some technical issues, I ended up with an offer at a balance sheet bank in the NY office for their M&A group.  Ideally, I don't want to stay at the bank and want to recruit for FT the following year at a BB/EB or even one of the top MM, and of course, I will try to get the return offer at the bank. 

I'm not familiar with the recruiting timeline. When should I start sending out emails?. Should I or should I not include the SA offer in my updated resume, like "Incoming SA at ...", and how do I form the networking emails, as well as what to talk about during the conversations ? Because people have told me I have to keep it low and cannot let the word spread or make it too obvious that I want to leave the bank. Anyone familiar with the process? Have you done a similar process? Please, any advice would be much appreciated. Thank you so much.