I helped Mimmo (owner of Aquila) with a bit of the development on the Banjo string sets. At one time he was sending out non-wound basses suitable for the set. The biggest problem was the diameter of the string required most people to file their nut slots wider to suit the unwound bass. Mimmo sent me two solid basses, one @ 1mm in dia and the other at 1.06. The 1.0mm (.039") was huge and barely would sit in the nut-slot on my banjo...but it did sound and play quite nicely.
The current "classical" set from Aquila features a silver-wound bass.
The only problem with the wound string is that it wears out very quickly on a fretted instrument. On my fretless...my set has been on for years.
If you want a solid (unwound) 4th, simply purchase a suitable nylon one from a guitar set. Singles are routinely available online from a number of string vendors like "stringsbymail" and "juststrings". I would pick a few in the 1mm range and give 'em a try. Savarez "yellow card" are well liked by a number of banjoists I know (they're playing more modern banjos though).
George, at a couple of the early banjo conferences stated that bridges for minstrel banjos should be of as light a mass as possible. I tend to use basswood, and have played with pine, poplar, and aspen. I've tried oak and maple, and did not like the sound as much.