Try to get on an earlier flight, you have the status to get that to work. If that's not an option, I would see what happens and if you can somehow make it (less delay, no lines at security - who knows?). If that does not look good (e.g. more delay than expected), directly call AA Exec desk on arrival and have them restore your flight schedule for tomorrow (both CLT and MIA have multiple options). Next, work with them for a stay, it may be that they have to pay for it - but you can even do that afterwards. Does this help?