Early April is kinda iffy weather wise but..... I was gonna say
Mammoth cave NP but you've been there so I suggest
I75 south rather than I65.
Check out Cumberland Falls state park.
Known as the Niagara of the south.
The campground there is
not the greatest. It's on the top of a ridge and pretty tight.
It can be done. I've seen motor homes in there as well as
larger trailers. I'm not sure what an 8316 is......
There are private CGs in the area.
Cumberland Falls can be SPECTACULAR in the spring if it's been
Here is a clip of the falls as seen after a 5 inch rain--
Big South Fork National Recreation area is close enough to
Cumberland Falls to day trip from one to the other.
Yahoo Falls is awesome. The highest water fall in the state.
Easy to walk to but also offers some trails if you want day hikes.
There is camping in Big South Fork here--
Big South Fork National River & Recreation Area - Campgrounds (U.S. National Park Service)
We've stayed at Blue Heron numerous times.
Great sight seeing in the area.
Day hikes, train ride, museums etc.
Don't miss visiting the Blue Heron Mining camp run by the
National Park Service.
The city of Sterns KY offers the Big South Fork railway and coal
museum. Well worth a stop
Big South Fork Scenic Railway - Stearns
Those are some of my suggestions..... Come to Kentucky, I came to visit
41 years ago and I'm still here!!