Brent,
As for route, you will want to take I65 south from Nashville through Birmingham to Montgomery then divert to Highway 231 south towards Dothan, AL (my first gas stop at the Flying J there), then Hwy 231 south into Florida, hit I10 headed east, and proceed to I75. Going that route, you pick up I10 at mile marker (mm) 130 and get to I75 at mm 298 (Tallahassee around mm 200). There is a whole lot of practically nothing between Tallahassee and I75.
That's the route I take and I live in the central Alabama region. I can't help you with campgrounds but like you we like to get close and spend the night before rolling into the Fort the next morning (we aim for Lake Louisa State Park in Clermont which leaves 30 minutes to the Fort). There is a KOA in Ozark, AL right along Hwy 231 (about 20 minutes before Dothan) which is right at 500 miles from Paducah (I don't know how many hours/distance you want to get in when you leave Paducah). That would leave about 400 miles to WDW from Ozark (back up nearly an hour if your destination is Ocala).
How far do you plan to drive the day you leave Paducah? and from that stop, is your next stop Ocala?
Bama Ed