To reproduce that profile as nearly as possible, I think you will have to start with the using some very straight wood to make the first, basic flat sections. Mitered, picture frame corners would be the easiest way. Once you cut to the exact lengths you can use a curved beading bit to make the rounded bead around the outside. (You could reverse that by cutting the long pieces a little over length, then putting the bead on the outside edge, and with the table saw trim the inside slightly to get that slight inside angle.
Put in the panel (I'd probably use ply), glue up nice and square, then use standard molding to as closely as possible replicate the inside beaded pieces, cut very carefully to fit. At least that's how I'd do it.
I'd reinforce the corners with splines. Theoretically you could make a lapped miter joint, but a spline in each corner will be much easier.
The chances of making a profile like this successfully in 30-50 ft of straight, 3/4 hardwood are pretty slim. I'd cut my own rail and style material, plane it flat and correct thickness, and get those doors together in 18 hours of less because those pieces are very likely to warp quickly. Make sure your oversize stock is sufficiently dry on purchase and stored for a week or two in you shop before you cut it.
I don't see this as a terribly complex project if you're using ply, but if you are going to use glued up panels, it will become more complicated fast. Nice project.
