I travel from Tampa to Key West several times a year. I take I 75 to exit 101, Naples, go about 6 miles on 951 to US 41.( North of this area, US 41 is a very urban road.) Go 82 miles and turn right on Krome Ave ( 997) for 22 miles and it'll put you right on US 1
41 is , to me , a much more pleasant drive than Alligator Alley ( I 75) and taking the route I do, you avoid all the crazy Miami area traffic.
Before I 75 was put in, I used to drive Tampa to Key West all the way on US 41.