First off, welcome to the forum
Are you sure it's done fermenting? That'd be the first step. Since you'll be pasteurizing (more on that in a second), it's not as crucial as it is with beer that you be sure it's done, but it is definitely best practice.
If you plan on backsweetening with the FAJC and caramel, and you want it carbonated, you DEFINITELY need to pasteurize.
Even if your fermentation is complete, adding more food for yeast (sugar) will cause fermentation to kick back up again. The problem is, when you've capped your bottles you don't allow CO2 to escape, which could (and with that amount of sugar probably will) cause bottle bombs. You want it to ferment a little bit (that's how carbonation happens), but if you allow it to ferment dry without pasteurizing, you will likely get bottle grenades.
My advice is to leave it in your carboy for as long as you can stand it. This recipe gets pretty good after it's been aged for a few months, and a few months after it's been in bottles it gets to be outstanding.
Hope that helps.