Hey Justin,
I also built a gourd banjo a few months back and am enjoying playing it immensely. Early on I managed to break my 5th string and did some research to try to match the string gauge. I remember that Brian noted in his documentation with the kit that yes, he used classical guitar strings for strings 1 – 4 with a wound 4th string. Also that he used 50 lb. test fishing line to match the guage of the 1st string. I finally found a chart that referenced guage of fishing line and that 50 lb. line guage is .028in. That means the 1st string should also be .028. I can’t remember guages of the other strings but I bet you can find a classical nylon string set where the 1st string is .028 and the other 3 should be pretty close to those included in the kit. BTW, my son being a fisherman, I asked him for a length of 50 lb. test which he didn’t have. But he did have 40 lb. so I used that to replace my broken 5th string and it seems to work just fine. It is .024 guage which is pretty close. Hope that helps. Good luck.