AMCAS submission timeline SOS

Ok here's the deal: so I re-took the MCAT on 5/18 and wasn't planning on submitting my primary for verification until 6/18 when I get my score back because God forbid anyone see just my first MCAT score. I have a strong GPA and ECs but just waiting and praying for a better score before I finish up my app and submit.

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I'm getting all nervous now that I'll be submitting too late. I looked at some SDN chart that said for 6/18 submission dates it takes ~32 days to get verified versus ~20 for people who submit on the first week. Would it be worth it for me to apply to one random school this week to speed up my verification process? Or will those 2 weeks not really matter in the grand scheme... anyways lmk your thoughts :)