Actually, I thought DME picked up anywhere between 3:15 and 2:45 before you flight. So it's possible your scheduled pickup time will be 5:45A. This is what you need to hope for.
With a 5:45A pickup time, you need to be at the loading area ready to go by 5:30A. If I were you and that were the case, I'd have all my checked bags at RAC at 5AM waiting for them to open. That gives you 30 minutes to get the bags checked before being at the loading zone.
I'm not sure what you're saying here... an 8:30A flight would be about the earliest (and it's iffy IMO) you could get bags checked for. A 12:30AM flight would be about the latest (figure checking bags at 12:30PM). So that gives you 16 hours of flight time. You don't have to have your bags checked 12 hours before your flight.