Well, my guess would be (for each door), 2 uprights, 2 cross pieces, 17
pieces for between the panes, grooves on the edge of each piece just
wide enough for the glass, and glue on all wood-wood contact points.
Assembly done on a large, flat surface starting with one upright and
both cross pieces. Maybe a tenon on the ends of the cross pieces and
the ends of the "between" pieces that connect to the uprights and cross
pieces. Tenon fits in the same groove as the glass. Work fast, and
clamp it flat and square.
Only thing that bothers me is the joints where the four pointed ends
come together between panes. How about grooving those as well and
putting a square piece in there to "key" the pieces together?
No doubt someone (perhaps everyone) else will have better ideas here.