I've been interested in Peter Lynn Arcs for kite boats at least because of their auto-zenith characteristic. They are also quite simple kites. But, to be honest, I've never been convinced of their aerodynamic performance. Perhaps I need to learn more about them - but too often they seem to drop to about 45° in the wind window and fly badly.
Notwithstanding these misgivings, an arc-stable sailing mode was investigated, inspired to some extent by the Liberty Kite of Beyond-The-Sea (Yves Parlier). With this rigging, one wing tip of the kite is tied off low to the deck. The other wing tip is tied off elsewhere on the vessel so that the line defined by the two tow points aligns with where the long kite lines would be if the kite were not constrained at the deck. The second tow point has a longer line in order to allow the kite orientation to be as in the video below - and thereby generate some thrust. In good wind and with good tow point alignment, the kite flies quite well with quite reasonable (ie small) oscillations. However, if the tow point alignment is poor, relative to the wind direction, the oscillations are quite large and usually end badly. An interesting exercise - but probably limited applicability.