A random search for March 12 yielded $138 for same-day connection versus $900+ for the overnight.

If you're not exceedingly risk averse, book MKE-CLT connecting to the last CLT-JAX flight of the day. Miss the CLT-JAX flight, then go to the gate or ticket counter after the flight closes, tell them you missed your flight, and ask to stand by on the first flight the next morning. Technically the Late Arrival Standby policy doesn't apply for the last flight of the day, so there's risk there, and there's risk that the next morning's flights will be full. So if you don't want those risks, do something else. But in all cases where I've missed the last flight of the day (whether my fault or the airline's e.g. delayed incoming flight), I've been put on standby (if not confirmed) for the next morning with little or no trouble.