Based on that last photo I can see why you thought it might have been a Carpenter Frog. I think you are right about it being a Greenhouse Frog.

The reason I was able to rule out carpenter frog (even though I am not too familiar with that species) is that the frog you posted as a number of characteristics not typical of the Rana (now Lithobates) genus. The hind feet are not webbed at all and the tips of the toes expand into little discs, much like a chorus or tree frog.

Using other characteristics it is possible to rule out every option except the Greenhouse Frog. In Florida your frogs are broken up into a number of distinct groups. It's not a toad or a treefrog. Looking at various characteristics I can tell that it's not a cricket frog (Acris), chorus frog (Pseudacris), or true frog (Rana). The only option left is Greenhouse Frog, as you thought.