My Lyon and Healy is a fretless 7 string.

I play all kinds of banjos, including fretless 5 string, but let me tell you, It's a real white elephant. Anything fretless is a real challenge, especially up the neck.
There are so many variations that count as banjos... I have an A.O. Oakley with two drones (not set up yet) which should prove to be
real riot to play. I know there are other similar 19th century banjos
with multiple drones. They built all kinds of variants before the banjo was standardized
Keep pickin' and don't be afraid of banjos that seem weird. I found my first 7 string leaning on a tree at a flea market in New Hampshire in 1989. It was stringless, and had no tailpiece or bridge, but I figured out the tuning. I just use any regular 5-string tuning, and tune the 5th and 6th strings as octaves to the 3rd and 4th. It had a skin head, and I set it up with classical guitar strings. I re-cut a standard 5 string bridge for it.
Also, if you closely examine your 7 string, you'll probably find that the frets were added later, sometimes right into the neck, with no fingerboard.

Banjarz7