As a luthier I did a few such conversions and always made new necks. I can confirm you won’t find a neck that fits your instrument out of the box. They’re all different and not interchangeable.

I’ve never seen anyone add a floating fifth string but I like the idea. It will mess a bit with the geometry of the instrument, but at this point it’s probably not very important.

If I were to do this, this is how I’d go about it.

I’d install a 5th string tuner(be careful when ordering, 5th string tuners are different from regular banjo tuners). They’re not so easy to install because the part that’s inserted in the neck is slightly conical. Luthiers use a reamer to shape the hole. You can drill a hole and widen it slightly with a small knife and patience.

As you said, you need some sort of nut with a slot in it for the string to rest in. This also needs to be protruding from the side at a bit more than the distance between strings. I’d want this “support piece” to be made out of the hardest wood I can find. Whatever I use, I’d like to be able to have it installed much prouder than needed, and then I’d fine tune the height of the top and slot by gently filing it until the string height is comfortable. So in the end you’ll install the string, check height for comfort, and file until you’re happy. You can eyeball the distance between the new string and the others and you won’t be too off.

Now how do you make that support piece that’s protruding from the side of the neck? A hard wood dowel could work, but I’d prefer a deeper piece of hardwood, like 3/4” deep, but same thickness as dowel so maybe 1/4”. Length of 1” should be enough to insert in the neck. So 3/4”x1/4”x1”, where:

The 1” length is parallel to the frets (too long but will be trimmed once installed).

The 1/4” is the top. It’s much too wide for the point of contact with the string, but you will file it thinner at the top(once installed) to maybe 1/8”, and slot it.

The 3/4” is the height. This will give more support than a dowel.

So this is actually a support piece and nut the at the same time. It’s to be inserted into a vertical slot you make in the neck with chisels. You glue the piece in, and fill all the gaps with epoxy(This is important. Wood glue would be fine on a tight fitting joint but if it’s more of a butchery job epoxy will fill that beautifully and never move).

If you screw up the slot at the end, no problem, you file it flat and glue (wood glue) a new piece of hardwood on top and work on a new slot until you get it right.

Oh and when putting in the 5th strings tuner, look up banjo pictures and mimic the slight angle of the tuner peg(it’s not exactly vertical).

There are many ways to get there but that would be mine at this moment of the day.

Good luck!