I want to vote, most definitely, in the primary but because I'm registered as

And the rules in that state

Ohio doesn't have Party registration and either party can vote in the others primary.

You may be able to register as a Dem for the primary and then reregister as an independent in time for the general.

On the other hand, since it's Florida, you might not want to mess too much with your registration at all.

Florida is a closed primary state. Only voters who are registered members of political parties may vote for respective party candidates for an office in a primary election.http://election.dos.state.fl.us/voting/voting-info.shtml

A bill that would enable Floridians to register to vote online, and, presumably, change their affiliation, too, is supposedly on the way to Rick Scott's desk for his signature.

As soon as he figures out how to keep poor people, African Americans, Native Indians, Hispanic people, and wimmen from getting access to computers, he may go ahead and sign it.

http://www.tampabay.com/news/politics/stateroundup/florida-house-approves-online-voter-registration-8212-with-a-twist/2227331

County election supervisors have been lobbying for the online system for months, but they are concerned that Scott might veto the bill (SB 228). His chief elections official, Secretary of State Ken Detzner, has spent the 2015 session trying to kill the bill, warning that "forces of evil" will try to disrupt Florida's election machinery in the 2016 presidential election.

Forces of evil already run Florida.

go directly to the election office and do it in person. Thank you all for your answers...