Zither banjos are usually English and uniformly awful. The neck problem and the poor tone (yours does have the small head sort of suspended in the center of the shell, kind of cradled in a resonator of sorts, right?). The light construction and the smaller head size, plus the non-reinforced neck, make for a hard-to-tune, plunky-is-the-best-tone-you-can-hope-for banjo.
I turned down a free one once, and would do so again if asked. They are curiosities, at best.
Now, that rant aside, it is possible to get the "best" out of them, and to make actual music on 'em. For curiosities, they are at least musical, unlike some of the Marx Co. instruments you occasionally see (Marxophone, Ukelin, Hawaiian tremeloa, etc.). Those were REAL junk, not just an average idea which caught on, like the zither banjo.