This is fascinating. I'm researching to do a sweet potato wine. I'd suggest country wine as a gluten free drink, and also mead. (Although the whole mashing thing is half the fun of making beer)
Here's my two cents on the awesome beer idea though. I've made banana wine, which was nearly undrinkable for all the body it had, so that'll give you some body, but be careful if you have any banana solids at all, that stuff foams like crazy and is like glue for an airlock - good way to redecorate your ceiling. Sweet potatoes i haven't tried, but potato wine, if sufficiently boiled, is totally fermentable without any enzymes, although you can taste the higher sugars in sweet potatoes, so the idea of mashing them is great.
I'd also suggest molasses as a possible adjunct; it has that real nice malty flavor, and the yeasts love it (in a starter at least). I'm excited to hear how this goes, and wish i'd looked at the date before i replied. Ok, good luck!
Oh ok it's not super old that's good! Also, regarding juicing: you get a whole lot more flavor and body by juicing vegetables than by just boiling them, so take that into account. You may not even need to worry about the body. Also it takes more time to clear.