I think the tinnyness is inevitable because of the way it's bowed close to the bridge pin so it brings out a higher harmonic, like bowing a violin too close to the bridge.

The Clemens Neuber patent for 1925 is for a 'violin zither' rather than a bowed psaltery as such; a very different beast with none of the mediaeval overtones of 'psaltery', though a differing sort of Volkishness as you suggest. Calling these things psalteries is pretty bogus; selling them as 'early' instruments (as the Early Music Shop has been doing since the 70s) even more so.

The violin zither still sounds pretty ghastly, the sound hardly improved by the chords:

http://www.youtube.com/watch?feature=player_embedded&v=nkfy0g6Ltsc