Gas Station:
If you're going to run out of gas, you can stop at the gas station, or stop when you run out; either way, you're gonna stop. Is the Gas Fairy going to bring you Gas at the side of the road? Unlikely. Is a Florida Cop going to be aware of, and concerned with, your Rights? Even less likely than the Gas Fairy.
Is it legal? Precedent exists for other regulated matters, but as to it's application to OC, there hasn't been a case that I know of.
It seems reasonable, but I'd say you'd have to fight an arrest and prosecution to get that precedent applied to this matter. Prosecutors here are quite zealous. They'll push anything they can. It would probably be dismissed, but you would definitely get arrested and prosecuted. Expect it to be a felony stop, and to be charged with a felony...
They may even shoot you and fix it in the report; your corpse cannot mount a defense. It may be easier to kill you than risk the 1983/42 business. If you're dead, then it's their story and only their story. FDLE teaches this, I was there.
It's a very risky move. If you don't value your life, and you have a whole bunch of money, then you might consider it. I wouldn't recommend it.