This is for the baglamas, the little mandolin-like instrument from Greece. I think it is such a wonderful sounding instrument!
My baglamas is made differently--the bowl is not made of a single block of wood but out of wood that is split and bent like an oud, or a bowl back mandolin. The headstock is also originally separate from the neck, like in the guitar.
With my little experience in lutherie, I would think to try it not by creating the whole instrument out of a single block of wood, but by creating the bowl (either via carving or bent wood), sharpening the neck to a spike and having the spike go through the bowl as in a banjo.
(But--would this be strong enough for the six steel strings? I also had an idea for a different sort of headstock today that would be interesting to experiment with--to have the strings wrap on the bottom, and then thread through to the top. I already have a homemade instrument that I might be able to convert this way.