Big box stores sell trim called "Screen Molding". It about 1/4 " thick and 3/4 " wide wood in 8 ft lengths. Paintable and stainable. They also sell screen material and wood glue. You may need to go to West Marine or online to get real brass or stainless steel angle brackets.
Put your hatch boards on a flat surface as they would be in the slot on the cabin and measure each edge's length and each corner's angle. Cut two sets of moulding strips to match. Lay hatch boards aside. Place first set of strips on flat surface, flat side down in proper orientation. Place angle brackets at each corner. Secure each bracket with screws only to, not through, the wood.
Go have a Beer.
Place the uncut screen material on a flat surface as big as the frame. Lay the frame, flat side down, onto the screen and mark the outer edge of the frame on the screen. Cut screen and turn the frame over. Clamp the screen material to the flat side of the frame at each corner. Use wood glue and the already partially affixed screws to attach the screen and the second set of moulding strips to the frame permanently. You're making a sandwich. The wood can then be stained or painted. I also sealed the wood frame with two part clear epoxy.
You want deluxe?
Extend your screen material at the top edge before cutting to cover the open hatch slider area as well. No frame, just attach velcro to that section at the edge of the screen and to the underside edge of the open hatch lip with contact cement.