M&A SA to Restructuring FT?

I will be a summer analyst in the M&A group at WF/Jefferies/UBS level firm in NYC this upcoming summer. Recently, I was introduced to the world of restructuring banking by an alum at PJT/HL/Laz and after learning more about it in the last few months, I am totally hooked on the field. However, is it possible to make this jump from my current position to Restructuring FT?

I am unsure how recruiting works for restructuring, and it seems that the top restructuring firms really only hire students from top targets (I am from a non-target, although my GPA is a 3.95+ from a top 20 liberal arts college). Do restructuring firms at PJT, HL, Laz, Evercore, Rothschild, and Greenhill even do FT recruiting? Any feedback or guidance on how to make this jump would be really helpful!