It is (or should be) very simple. The interior of my vehicle is not my employer’s property. I see no clash between my right to carry and my employer’s private property rights.
Your vehicle is still within the boundaries of their property, so any gun you would have in your car on their property would still be on their property.
Your person is your own property as well, however if you carry something on your person and enter someone else's property, you are taking that item onto their property.
You can't just put blinders on and say that the conflict doesn't exist, just because you wish it didn't.
There is unquestionably a conflict between the rights of the property owner and the rights of the employees.
Both the property owners and the employees are private individuals.
It is because the rights of individuals come in conflict when they interact that we need laws that govern how such conflicts are resolved.
Fortunately, the Florida legislature appears to be trying to do more to affirm the right of individuals to protect themselves, though it is at the cost of the rights of the property owners.