Night shooter, the bottom line is this. You live in FL. There is no such thing as pre-ban or post-ban. It doesn't exist, you can proceed in life like there was never such a thing. What is on the AAC website with regard to pre and post ban does not apply to you so making a phone call to them is pointless. Most of the states that have AWB still in place you can't legally own a suppressor anyway so again, the statement is pointless and so is asking them about it.
In FL, as in the majority of the other states(34 I think) private ownership of silencers is legal. FL is one of the 34. You can buy the silencer from a SOT(special occupational taxpayer), or an individual in your state. You would do so on a Form 4 filled out and sent in to the ATF NFA Branch in duplicate. A person is defined as a partnership, company, association,
trust, estate, or corporation, as well as a natural person. If you submit the form 4 as a natural person you will have to obtain CLEO certification(sign off) on the form as well as submit a fingerprint card and color photographs. Also a check made payable to BATFE for $200. You also have to send a Certificate of Compliance form 5330.20 stating you are a US Citizen. If you submit the form through a trust or LLC, no photos, fingerprints or CLEO signoff are required.
If you can legally own a firearm, in about 30 days you will get an approved form 4 back with a $200 tax stamped affixed to it. At that time, you can take possession of the silencer and be on your way.