I know. My wife and I were shocked as that was one thing we never considered. Interestingly, I went onto the NY Consulate site to consider going there. Sure enough, it states that it will only service those in specific surrounding states.
I've just visited the US Embassy BKK website and learned that the FBI check can be done from here. Well, part of it... You can have the fingerprinting done here and then send the fingerprint card and application to the FBI in the States, along with the $18 fee payable via credit card (downloadable form). Include an email or phone number and allow 12 weeks for processing. If fingerprints are required by the state of FL, I'm going this route...
I am flying into LAX and have 2 full days there. But I can't do anything without having the background verification in hand to submit. I've emailed the department in FL hoping for clarification on how to proceed from here. I'll update here when they've replied...
It now needs to be issued by a state, or the FBI. And it needs to be signed, as per the Washington, DC webpage. I've contacted the state of Florida in order to see what they require.