As Carol said, changing your flights (if possible) is probably your best option.

In my personal experiences with CLT, the wait for luggage has NOT been a problem. I know it has for others but in my personal cases (and I think many other travelers also) the bigger issue has been with waiting for a gate and/or the time it takes to clear customs and immigration.

Carry on or not, luggage service or not, nothing is going to change the actual time it will take to get through immigration. If your flight is delayed for any reason, if you have to wait for a gate or if you have to wait to deplane due to the immigration hall being full, the luggage is likely NOT going to be an issue.