Can't speak for NFHS, but I'll take a stab at the ASA answer. Correct me if I'm wrong. And remember, I'm SP-only.
When the pitcher committed the IP, we've got a DDB. Then, we have the runner leaving the base too soon (not a violation of the LBR). Once the runner left the base, the ball immediately becomes dead.
Enforce both. The pitcher committed the infraction, so a ball is awarded to the batter, and the runners advance. Then, enforce the runner leaving early AFTER enforcing the IP.
Why is that important?
Well, what if there were two outs with a runner on 3B?
Am I right? Or am I smoking crack?