Sent a faulty resume on an email application; is it a bad idea to try and resend a better version?

Here's the lowdown:

A year ago, in my last semester as a student I participated in an intern program ran by my school where I was simultaneously a student with a collegiate adviser and an intern with an independent company in Washington, D.C.. That collegiate adviser and I are still very close, and he knows that I've been itching to move back to D.C. for work. He recommended I apply for a contracting fellowship at a company division presided by an older alumni of the program I was in and that he advises for. He said that the alumni was explicitly invested in hiring other alumni of the same program.

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I submitted a resume and cover letter via email a week and a half ago; the cover letter was great, but I've really professionalized my resume since and upon review the one I sent was actually really shotty and I'm anxious that they won't seriously consider my application because of it. As a bonus, I looked at the alumni's LinkedIn profile without realizing it notified him, and he reviewed mine three days ago. My profile is a bit of a mess and before today didn't accurately reflect some of what I put on my application.

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I'm glad to have learned a few key lessons from this, but the position is really attractive and I feel that aside from the LinkedIn and resume goofs I'm a serious candidate; especially with our shared alumni status. I'd like to try and salvage the situation if I can.

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I was thinking about: messaging the executive on LinkedIn and trying to professionally emphasize/restate my interest in the position, or emailing the application address with an updated resume and the same cover letter and some sort of clarification/excuse. An example would be that I recently moved back home, and I could say that I was emailing them a resume with an updated location.

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Would either of those two options feasibly pose a chance of helping me to correct the situation? Or am I better off waiting and hoping my cover letter/alumni status carries enough weight? I'm new to the professional job market and feeling a bit lost.

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Thanks so much!

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