Thanks! The folks at Edensaw Woods recommend ash, so I went with that.
I assume that the glue (Titebond III) on the back side of the edge banding counts as sealing that side. I'm going to start with epoxy on all of the end grain and then paint. Most of the door structure is engineered wood (LSL 2x4 and 2x6 stock for the frame) and marine plywood for the faces. So, I'm hoping that most of the movement will be limited to the edge banding and trim. I'm a bit worried about shearing forces (since I don't think the door slab will move much), so I'm planning on mechanical fasteners for the (12 mm) edge banding.