There is a few things to think about, and I'm going to lay them out all at once.
A bicycle is a bicycle, no matter if you put a gas or electric motor on it. Electric in Florida is regulated, but gas is not.
Motorized bicycles aren't mopeds - mopeds come with vins and mcos, and when registered are generally registered as motorcycles - unless that state has regulations not requiring registration, or requiring a type of registration for mopeds specifically.
Were you to get a vin for your motorized bicycle, you would have to bring it up to federal safety guidelines and get a state issued vin. It's not too much trouble aside from getting it up to snuff, but it is not necessary.
As has been said before - laws are not written to make something legal, they are written to make things illegal and to regulate. There doesn't need to be a law written to make something legal.
Stick to bicycle laws on gas and keep it under the posted speed limit. Ride as though you represent the community, and be willing to fight any tickets. It is not up to you to prove your innocence, it's up to the state to prove your guilt and that you are in violation of any laws. If those laws don't exist - it's just wishful thinking by the law enforcement.
And in the necessary addendum - you guys need to make some propostitions to protect motor assisted bicycling - by both getting gas regulations written and by trying to get some leniency on electric.