Curious: when you run a sling, are you swimming out of it when putting it to use? It should only go around your neck (wear a collared shirt to save your neck from abrasions) so it doesn't get in the way of high-ready or cross-shouldering, but you can still go hands free for a moment and it doesn't drop to the ground. When out of use, swim back in and secure it so you can go hands-free without it getting in the way.

During training, I was under the incorrect assumption that a sling should be used for stabilizing my shots and was taught that's not ideal for most scenarios because of how it limits your versatility of ready and shooting positions.