It's really a non-issue in Florida anyway. Those "no firearms" signs are not weighted by law. Meaning, they only serve to inform you of the property owner's wishes.
It's up to you how to react. You can take your business and leave. You can go back to your car and disarm. Or, you can ignore their stupid, meaningless sign and not give the uneducated any power over you, your daily activities, or your freedoms.
ME? I look for them so I'm informed, but, I ignore them completely. I won't let them infringe upon my freedom. I'm not about to turn around, take time out of MY day to go somewhere else. What the morons don't know, won't hurt them. Concealed is concealed.
And, if, for some reason, I get discovered, I'll leave. Simple as that. But, I've broken no laws. (Unless it's a prohibited place by state statute, which I wouldn't do anyway.) .
Only AFTER I'm done with them will I make the choice to boycott. I just won't return. But, as I say, I'm not about to let them bully me into disarming OR finding somewhere else.
If I'm in a particularly foul mood, I will catch the manager on the way out and inform him/her of why they'll never see me again.