I've contemplated this upgrade too. I haven't got around to it yet, but have pretty much decided that when I do, I will not have the doors "replace" the boards.
Instead, I will mount the new doors just aft of the track for the boards. That way, we would use the doors for the most part while aboard, but still be able to drop the boards in place for more security (against weather, theft, etc).
I plan to build the doors with the screens permanently affixed, but have them somewhat recessed in a rabbet (as SD described) so that the acrylic windows (with gasket) can be set in place over them as needed. They'll be held in place by little wooden twisty toggle thingies.
Here is one vendor of companionway screens, etc, that might give you some ideas:
Glebe Creek Screenworks