Unwrapping in the cooler won't accomplish anything - the moisture is still there. The cooler time is 1. to hold the heat until you're ready to eat and/or 2. to finish off the last of the tenderizing - so unwrapping is futile.
If you get good product without cooler time then don't change!! :D
Putting a brisket on the grill after I've worked 8-12 hours - I don't think so! The extra handling would tend to rub the bark off. You usually don't have an extra grill at a cook off and time is the one thing that is in really short supply!
At competition the more you handle the product the bigger chance you'll fark it up, drop it, overcook it, or burn it.
That's the reason we're kicking this around in the COMPETITION forum - drier cooking to near the very end is probably the answer - foil only if you have to before prep. What we do at cook offs is not necessarily what we do at home -- for example: my fall off the bone ribs at home!!
Southern Brethren BBQ Competition Team
"It's all about getting paid!" - Myron Mixon
"I love being hated in my hometown!" - David Hair
KingFisher Gator Rotisserie cooker, WSM, Stainless 5 burner with IR gas grill, Turkey Fryer, Weber JD Commemorative grill, slightly used Bandera chamber for future use as a cold smoker, Masterbuilt 40" insulated ELECTRIC smoker