Meet with a local criminal defense counsel and explore a legal eligibility to either seal or expunge your records.
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You can move to expunge it. Meet with a local attorney to inquire about it. The Florida statute requires that you disclose even if expunged when certain institutions such as the military inquire. I also believe that Homeland security has access to records that are expunged.
My thought is that the military background check will turn it up even if expunged. You can't "destroy" the record. You should ask the ROTC program if your prior will keep you out. They may even know of people who got in with what you have, or know lawyers who can help you seal/expunge your record.
This general legal advice does not create an attorney-client relationship. Every case is individual and to have legal advice that you can rely on you need to talk to an attorney one on one, answer their questions, and hire them.