With a tow vehicle I would use the map listings campgrounds on the Allstays website and look a little farther out from your target area.
Possibly look around the Dade City/Zephyrhills/Spring Hill (to the north) your target area.
I would avoid I-4 and Lakeland area as that is always packed because of the I-4 corridor and proximity to Disney. Here's the link to the Allstays Florida campground map.
https://www.allstays.com/Campgrounds/Florida-campground-map.htm
"The only time you should fear cast iron is if your wife is fixin' to hit you with it."-Kent Rollins
First law of science: don't spit into the wind.
Magnus