No offence but I would forget the router idea, in the tine it takes you to ask the questions, sort though the responses, make templates, set things up, do a practice run, etc... you could have the barrel in and be working on the architecture. Even if you do get a jig set up, are you going to use the same barrel over and over or is this is a one time build and then a new jig for the next, same process.
Routers may have a place (Not sure where that is, maybe in a box on a shelf) but they can defiantly ruin your day.
Not trying to discourage you just trying to give you things to think about.
Tim C.
PS: In the late '70s I built a table that used a router to ride on rails, it used two bits, a straight and a 45 deg. It took a long time to get it set right and many passes with shallow cuts (straight grain is one thing but add a little curl and pullout/chips will really ruin your day) to get it right and that was only for straight sided barrels. TC