Robert thats a good point.
Its worth remembering that all alien home owners in Florida have their foreign address details (if they gave them in the first place which may or may not be compulsory, I can't remember) on a public database which can be searched and can even be bought as a CD.
Thats why if you are a Brit owning a home here you receive occasional junk mail at your UK address from realtors and remortgage companies.
It would be easy for any lawyer to look up those details and then maybe take action against your assets in the UK.
I was actually liasing with the Osceola County Property Tax Appraisers Office a year or two ago about this but before I got anywhere the head honcho Bob Day got arrested for all sorts of things so that was the end of that.
I don't think there is any way you can get off that database, there ain't much privacy here.
All I can say is don't give your UK details to anyone here if you can avoid it.

And yes, make sure you have a decent amount of personal injury insurance on your car policy. What is a decent amount? A million doesn't go far if you put soemone in a wheelchair for the rest of their life. Nor does ten million.

I think even rental car insurance - which the big companies often don't actually have with an insurance company, they bear the risk themselves to retain the profit within their own company - has its limits although they are high.
So unlike the UK there is no such thing as risk free driving when it comes to the possibility of a claim being made against you in excess of your policy benefits.