Hello Scott,
Firstly I have to ask why you don't want to make these doors as one piece MDF? I know that the back wouldn't match a traditional 5 piece door but it seems like the savings in machine and assembly time would significantly reduce your cost which your customers may appreciate more than they value the 5 piece aesthetic.
If you are committed to producing a door that looks like a 5 piece door, you might consider making a 2 piece door. For shaker profiles similar to the photo you posted it would be very simple. You would cut a frame from 3/4" MDF. This would have a 3/8" deep rebate around the inside of the frame, "squared up" with a 1/8" or 1/16" diameter tool. Then cut your centre panel from 3/8" MDF using a ball nose tool in the way Jared explains. These panels should be cut around 0.01" smaller than the opening and have a radius in the corners that matches the radius of the tool used to cut out the rebate in the frame. I have found that these fit so snugly it's hard to tell that it's 2 pieces. This method is very simple even without costly software. You can easily draw up a template in any free CAD program and stretch to the required sizes before importing into your CAM software and assigning tools. There would be a slightly reduced yield compared to your 5 piece door and a small radius on the inside corners but your assembly and machining time should be greatly reduced.
I understand if you're set on your 5-piece concept but I figure it's always good to look at other options even if you end up rejecting them.