Trying to break into IB (Currently a Data Analyst)

Hello WSO!

I am currently a data analyst trying to break into IB and I am trying to relocate to Chicago, Il (at own expense).
It is my understanding that trying to land a position with a BB firm is likely impossible for me at this point. (Non target school, few connections, undergrad GPA not great but not awful). I would appreciate any advice that would help me land an IB role.
A couple questions I have are:
Is cold calling/emailing a viable strategy? If so, should I be targeting analyst, associates, or MDs? (I know the individuals in the field are very busy and i want to be considerate of that.
What kind of script should I follow? I am no longer a student and most of the post on here are geared towards students trying to become monkeys.
Are there any boutique firms in particular that I should try for?

Thanks in advance!