The way I normally recommend doing this is for you to take notes about your current Asterisk connections and reinstall from one of the distros. This way, you get tested versions of all of the support software as well as making sure that all of the settings in your PBX match up with the Asterisk settings.
The problem you are likely to run into the way you want to proceed is that a lot of your basic configuration information is not in the right configuration files. Since you’ve had to ‘hand craft’ everything you have now, none of these settings will carry over into FreePBX cleanly. Reinstalling from a distro and configuring everything from the GUI will ensure you can manage the system cleanly.