Rate my Profile for PE Recruiting

There's conflicting information on WSO as to how much one's bank/group affects recruiting, particularly for MF/UMM PE post-IB. I've heard people cite university, GPA, SAT/ACT, interviewing skills, and network as other very important factors.

To not only help me but others on this forum get an idea of how all of these factors are weighed in PE recruiting, I present my profile:

School: Top Target

Likely GPA: 3.7-4.0

SAT/ACT: 1500+ / 34+

Bank: mid-tier BB incoming SA 

Group: TBD, most alumni are in above-average or very above-average groups

Network: Involved in preprofessional clubs through which I've met upperclassmen going into IB/PE

Interviewing skills: I'm a grinder, and I think with the time I have I could get killer at timed LBOs and feel like I can tell a great story about why PE/why I see myself in an investing role rather than pure advisory.

And, not sure this matters: Non-diversity

tl;dr: Will being at a mid-tier BB put me at a noticeable disadvantage compared to peers applying for PE Associate roles from top BB/EB analyst programs? Does the group I get matter a lot? How can I stand out? Any other advice welcome.

I anticipate one of you will say "get the FT offer first/don't get ahead of yourself"--completely agree, but I still think it is valid to be thinking about my career and ask for advice from those who have gone through this process but aren't in my immediate network.

Humbly, 

A Prospect