I don't think they make a stringset for C tuned bari with wound strings....
Hello Patrick - Yes we do!
The set we had that gives
g c' e' a' on a Baritone (&
a d' f#' b on a Tenor) was called our "Linear Ukulele Set". When we updated the site, all the linear sets got new names like the reentrant sets, in other words, "Light", "Medium" etc. That set is now the LL-NW (Light Gauge Linear - no wound strings) set.
We also, however added another set for those tunings - our first with a single wound string. It's called the LL-RW (for "round wound") and has a polished round wound 4th string only.
We've never liked a single wound set on more standard gauges, as the wound 4th (lots of clarity - lots of sustain) next to a relatively heavy plain 3rd (somewhat muddy - not much sustain) makes the 4th sound like a duck out of water, and throws off the balance of the whole set. In other words, the 4-3 transition is awful. It's smoother if the wound/plain transition is a 3-2, as the second string is much livlier than a plain 3rd.
With this light gauge set, however, the 3rd is closer to the response of a normal gauge 2nd string, so in this case, a 4-3 transition works fine.
Compared to the NW set, the RWs are a little brighter overall. We didn't change just one string - the entire set is different. It also has a touch more tension. It's likely that if your Baritone has a build on the heavier side, it will respond better to RWs.