My advice would be to gather all your applications and ask your attorney who is representing you in the DUI case which schools you will need to inform. Maybe you get charged for an extra couple hours of work, but at least it will help you get past this and on to the rest of your life. Good Luck!
My favorite is a drink I invented. It is a Pirate Shot. 4 ounces bad Vodka, 4 ounces Kool Aid in an 8 ounce shot glass. Shoot 2-3 of these in 5 minutes and your night is guaranteed to be one filled with drunken fun.
From my experience, my applications have roughly a month turnover from when my reports were requested. But to be safe, double check the number LOR's required. This can be found in online services of the lsac website. But it sounds like you should be fine.
If your diversion is like mine, the charges actually were never filed. In my case the charge were put on hold. If I complied, they were dropped. If I didn't they were persued. So I think you are okay. In my addendum, I was clear about charges being dropped. You should make sure, but I think you would be correct to say this.