I am doing this but using classical guitar strings. However mine work out to D tuning - low A, D, F#, and B. I use the middle four classical guitar strings, and they are very slack due to the shorter scale, but work nicely for me - I try to play them softly.
I did it before using the low four guitar strings, tuned to C tuning, low G, C, E, A. The scale length of the bari made the tension for these the same as a guitar because the scale length of the bari is about the same as the guitar at the third fret - G, C, F, Bb, becomes G, C, E, A. This was a little too much for the bari - not dangerous, but didn't sound good on mine because the uke soundboard is thinner and smaller. These were hard tension folk strings though, what I didn't do was buy lighter guitar strings. If you did that, and tried both normal tension or low tension classical strings, I'm sure one would work for you.
Now, the other thing is, you want it re-entrant, so the low G is to become a high G. So try buying single strings at Elderly or your local store.
you'd want:
first string - Classical G string, light tension
second string - Classical D string, light tension
third string - Classical A string, light tension
fourth string - Classical G string, normal tension
I also did a fishing line recipe, and they sounded pretty good for re-entrant, but tuned to A, not G. G was too slack. So if you could live with one in A, try fishing line:
first string - 40 lb
second string - 60 lb
third string - 80 lb
fourth string - 50 lb
I highly recommend P-line string, I use it on all my sopranos that don't have natural gut. Other brands sound cheap and hollow. I use them because they play and sound better, and last longer, than any uke strings I've tried (although they squeak a little at first). Made by G Pucci and Sons, they are premium fishing line most fisherman can't afford. They are a co-polymer, part flourocarbon and part nylon, and are tough as hell. Bright and strong like flouro, yet supple and pretty like nylon, the best of both. Only problem is you have to tune them up, C tuning is too slack for them to sound right on a soprano. Works for concert though, and probably for tenor too.
The 80 lb is only available in large rolls, $130 or so for 800 yards. But if you have a good fishing store they'll spool out 50 or 100 yards for a few bucks, I spent about $25 for 100 yards of all four, and I'm set for life. I haven't changed strings in at least two years and they still sound great.
If you want to try fishing line for a re-entrant string in C tuning, you could take a classical set for the first 3:
first string - classical light or normal tension, G string
second string - classical light or normal tension, D string
third string - classical light or normal tension, A string
fourth string - fishing line, 50 lb or 60 lb
another brand of fishing line that was not bad, and maybe more common, is called "First String".
You're going to have to try several on your instrument to see what works best, scale, thickness, bridge type, material, all make a difference.
