A sleeper place to try is Big T's on Blue Parkway, just a couple blocks southeast of LC's BBQ. This would be just a couple miles south of the sports complex, and reachable right off of I-435 on Blue Parkway. If Gates is crazy busy, this would be a good back up plan. I like their BBQ a lot.
https://www.yelp.com/biz/big-ts-kansas-city-2