B-School Useful for FIG PE Transition?

Hey all - I am wondering whether going to Wharton will facilitate a transition back to PE. My background is that I did a Big 10 school, top BB FIG group on the street (2 years), upper MM PE (e.g. CD&R, H&F, etc.) for 1.5 years, and then a startup M&A shop focused on FIG. Note that for the latter move, the leadership of the firm was intending to create a merchant bank, where I would be able to also do investing alongside advisory. However, due to non-compete and legal issues that a senior partner encountered, it never panned out.

I would like to go back to FIG-focused PE investing. I applied to H/S, got rejected from the former and TBD for the latter. But should I also apply to Wharton round 2? Assuming I can get in, will my ~1.5 years at the FIG-focused M&A boutique make it more difficult for me to get back to PE? Or is my associate experience at the MM fund sufficient to get a foot in the door for interviews? Would going to Wharton be additive vs trying to just recruit straight into FIG PE and bypassing Wharton?

Thanks in advance!