That ball is bouncing all over the place. you may see it again sometime later. I will have to say that this situation described by the OP is one of THE most common things you will see in unemployment. "I thought I had the new job, so I quit the old job, then they told me I was not hired on the new job. Now the old job doesn't want me back."
It depends. It is a real chrystal ball thing. But until you have actually signed something, filled out paperwork, based on my life experiences, I would never tell you to burn your bridges, hire your moving company, cancel your lease. I"ve seen this happen SO many times.
It sounds to me like you might as well go move to Florida anyhow now, since you 've made all the prep for doing so. The next job in Florida may be the one you get. If your employer says no, you cant come back, and you do get approved for benefits, you can transfer your claim to Florida easily.
First of all, filing for unemployment may determine if your old employer is going to state yes or no, whether they can take you back. File for your unemployment benefits, and explain the situation. They will contact the old employer to verify the reason you left. This may worry the old employer enough to galvanize them into hiring you back, since you are already trained and they do not have a replacement set up yet. It will be from their employer tax account wages that you will be drawing benefits if you are to be approved, so perhaps this will be added incentive for them.
This is a maybe. It might be approved. You can show them, bring in the documentation where you cancelled your lease, anything you filled out for the new job that appears to be an acceptance, explain how there was nothing on your record that you felt would stop the hiring process. You are out of work "through no fault of your own," sort of. You did jump the gun just a tiny tad, no written acceptance, but you were certainly given a verbal assurance. File it, you certainly have nothing to lose.