I flew Spirit from AC to Fort Myers last month. I was nervous going into it, as it was my first time, but I had no issues at all. I used a Pelican Storm im2050 case. Make sure you don't use TSA locks on the firearm case. I used a set of Keyed Master Locks (model 131T). Had a second set of locks in my luggage just in case. I printed out a copy of my pistol purchase permit an kept it in the pelican case. I did lock my luggage with a TSA lock, but the ticket lady made it seem like it isn't necessary. I also printed out the TSA and Spirit instructions for flying with a firearm, and kept them in my luggage. I did not fly with ammo since my parents own a house in Florida, so I just bought my ammo while I was down there.
You just walk up to the ticket counter and say "you need to declare and unloaded firearm." The person working the counter didn't flinch, they just filled out an orange tag, you put your signature on it two or three times. Then they ask you to put the tag on the firearm case. They hand you a firearms declaration receipt and keep one for themselves. The lady did ask me the if firearm was unloaded, but they never asked to see the case. I also have a sticker on my firearm case with my name and number just in case they need to contact me. Made it out of AC without any problems. The process is much easier than you make it out to be in your mind.
Flying from Ft Myers to AC, the process was exactly the same, but the guy at the ticket counter didn't seem as comfortable with declaring a firearm. Seemed a bit nervous when I said I had to declare an unloaded firearm. Don't know if it was because he was new, or because he was a foreigner. But, no issues on the way home either.