After struggling with this problem for a while (see initial efforts at: http://community.wolfram.com/groups/-/m/t/1078687 and http://community.wolfram.com/groups/-/m/t/1097057);
I want to share a solution to this problem via the attached Mathematica workbook:
"A solution to the Four-Color Theorem applied to the map Florida, USA.nb".
The problem was not with the code itself but, with the way how the bordering counties for Okeechobee and Palm Beach are presently defined. If you remove Okeechobee from the list of bordering counties of Palm Beach (and vice versa) the code works.