We drive from Denver, so we pass right through KC. KC to STL is about 4 hrs, then we drive down to Nashville (good place for overnight stop), then down to Southern GA (another good overnight stop), and then onto Orlando (about 5 hrs)...just in time for check in.
I-70 to I-64 to I-57 to I-24 to I-75
KC to the Fort should be about 1310 miles
word to the wise: if possible avoid Nashville and Atlanta during rush hours (night preferable), especially if you are towing a trailer. I've driven in L.A., S.F. Wash DC, Philly, N.Y.C., L.Vegas, StL, K.C., but ATL and Nash traffic rush hour really sucks. Nashville = construction and traffic. Atlanta = MASSIVE traffic.
Hope this helps