advice to extend layover in ATL for meeting?

I’m flying from florida to SC and connecting in atlanta. landing in the morning around 9am and trying to attend a meeting and finish my layover later in the day. All logic points to this being no big deal, but Delta can’t extend my layover to say 6/7pm even though I’m already in ATL. They would rather I purchase a separate one way for later in the day (of course). Any advice what to do when I land from my first segment to take care of business and get on a later flight home?