Wait as long as you can without chancing a DQ for late entry. At first this will seem hectic and stressful, but eventually you'll get the hang of it and even catch the front end of the turn-in window often. You mentioned slicing, so I'm guessing you're thinking about brisket. We wait until ten minutes (1:20PM) before turn-in to slice and test our briskets. Briskets dry out very quickly when sliced, especially out in the wind. We wait so long because we want hot food for the judges. Although they are instructed not to judge based on temperature, which tastes better, cold/room temp beef or hot beef? They may not do it intentionally, but psychologically they will like the warmer product if all other things are equal. Above all else though, don't get a DQ. You've got no shot to win a contest without that score.
Rod, very nice post. Stop by the Cattle Call Forum and introduce yourself.