Fl. tax collector (that's what they call their DMV) will sell you those temp. tags direct as well if you're dealing with a private sale. Not sure I'd want to buy/drive on those for months though.
Not sure if Ohio offers it or not, but Mi. has an office for military and out of state residents to handle situations just like this one. Surprisingly, an absolute pleasure to deal with.
You send them your check or credit card info, bill of sale and signed title, they send you your plates and registration to your Mi home or temp out of state address.
Bottom line, there's a way to get 'er done. I wouldn't hesitate to give a plan like that a go. If you're considering this plan to get a "rust free Fl. car", make sure to run a Carfax on it to check it's history/verify you aren't looking at a car that just came from the rust belt (or flooded area).... You would not be the first to be burnt this way.
1997 37' HR Endeavor, 275hp Cat, Freightliner
03 CR-V Blue Ox, Ready Brake