I got started on the doors over the week and a half or so. Probably about 4-5 hours in or so and I'm almost ready for stain. I decided on leftover LP SmartSide 5/4x4 trim boards as the frame, osb backing, and 3/8 Pine panel siding for the outside panel, trimmed out in cedar. Inside the frame I form fit 1" foam board.
The idea is that using mostly exterior grade, manufactured products and thin panels to hopefully reduce the chance of warping. Also the foam core should help resist warping as well. I'm not sure if the LP trim is going to be as rigid as I want it to be but the doors feel pretty solid right now.
The doors are built with a half-inch gap all around and between the doors. Although I think I may have actually cut them a hair smaller, it's better to be too small than too big on shed doors. If they're too snug you won't be able to operate them individually and I can fill any gaps with jamb trim and weather strip.
Cut my panels to size, cut the trim boards to frame it, glued and screwed with triple-coated deck screws.
Foam core cut to fit. As best I could
Pine siding panel glued and screwed to the top.
Cedar trim to make it look nice-ish. I was one board short for the cross member.
Seems like most complaints with outswing doors are having to shovel them out in the winter, and snow and ice building up on the threshold making them difficult to open and close. I fit the bottom member with a 1" overlap that will protect the threshold from getting any ice and snow in it. The doors will mount to the 5/4 trim that already overlaps the foundation and threshold. This should leave about a half in gap on the overlapping trim boards that I can just fill with weatherstripping or just leave it and seal it at the bottom of the door.
I also cut a 15-degree bevel on the bottom rail and the vertical stiles to match. I've read that most rot on the trim comes from water pooling on flat horizontal surfaces. I didn't bother at the top because it's so close to the eve and there's drip edge over it I don't see it being a problem. But it would be easy enough to do after the fact. I'll do the same with the cross bar when I pop it on later today.