To start, it looks like Missouri does have reciprocity with FL, so if you have a FL permit, I would venture to guess you are legal.
Having said that, I am not an attorney nor do I play one on TV. You may want to call one to find out for sure. The question really is if Missouri will still recognize a reciprocal permit when they won't issue, and I would be hesitant to even venture a guess because if the complexity here, and the myriad of "it depends" criteria.
The other element here is to consider the circumstance where you are CC, and have reason to draw your firearm. Would you rather be judged for having done something to protect yourself or be mugged (or worse) in the event you opt not to carry?