Mike, yes you zero'd in on the most difficult part - those joints.. It takes some careful layout and attention, but they are definitely doable.
First to square up on the terminology, the two verticals are called stiles and the two horizontal pieces (curved in this case) are the rails.
First step, make a pattern from hardboard that fits the radius inside and out. Put an arrow on the pattern that points toward the keel or centerline of the hull. Make it 2 inches longer than the intended length of the rail. This dimension can be determined by measuring the door opening and subtracting the width of each stile. As mentioned add an inch to each end, this is needed for laying out the joints. This will be the pattern for the upper and lower rail, so make sure it fits nice, sand it in until it mirrors smoothly.
The two curved rails are band-sawed from 2" thick white oak, these are totally unsupported, so they can warp if not made without tension. Laminated; Pieces tend to relax when pulled off the jig, as wood has a memory. Steam bent; again the wood has a memory. Sawing the wood in state is best route to keep it from moving later on, from bouts of humidity and heat. Try to find some grain in the plank, that already has some curvature. trace your pattern, and remember to mark one top and one bottom with the arrow on each. Saw them out and drum sand them smooth, check them to the opening near where they will go left and right, use the best one for top. Also, make sure the thickness is observed, it must be to make the internal dado come out correctly.
Next, make the stiles. Which are just full 1" X 3". Cut a 1/2" dado on the inner side full length, 1/2" deep on center for the tongue and groove. Also, due to the angle at the jamb, the latching side of the stile must be cut at 22 degrees to provide clearance for the swing. The jambs are cut to parallel the angle to mate. If the doors and jamb have a 90 degree edge, they won't open. The hinge side can be 90 degrees. On this, I cut both side at 22 degrees as I did not know which would be best to swing from. The whole wheelhouse is built at an 88 degree angle back to the water line and wheelhouse floor. Back to making the stiles, They need a notch at each end to accept the end of the rail. Just measure in on each end 2" (the width of the rail) and mark. USe a protractor on 45 degrees, mark the mitre. Then notch out 1/2" deep in the bandsaw. Now, clean these up with good sharp files, establishing one half the joint, nice square and clean, now we only need to fit the rails to them.
Now back to the curved rails. Determine which side need the dado. Some scrap from the 2" plank with the same curve can be used to clamp each rail to the bench, as it will have the radius one side, and straight the other side. Now C-clamp a flat bar , perhaps a machine parallel to the base of your trim router, making a fence. Use a 1/2" bit and take light passes increasing depth until the dado is 1/2" deep. Like 1/16" per pass. Go in a direction (Right to left)where the cutter rotation will hold the work to the fence, only go in that direction, start from one end, go to the other and exit. When the dados are 1/2" deep on both, they are ready to fit.
With 4 C-clamps plus rails and stiles, go to the opening. Use some thin wedges to secure the stiles in place fore and aft. Now using the C-clamps, set the rails in place, lapped at the corners and secure. Now, once they are where they go, it's time to mark out how they will fit to the stiles. with a good sharp pencil mark it out from the back side. Leave everything as is and use a good scale or tape measure, and get a good measurement across from one stile to the other, at the innermost corner of the pocket to innermost corner of pocket. Record the measurement right on the rail.
Now, remove the clamps, get the two rails. Okay, you have layout lines which depict the angle and mitre, unfortunately, the rail would be too short if cut on those lines, so they must be transferred to the other side of the rail. Using a square over the edge transfer across. Using a protractor, copy the angle and scribe it on the other side. Now, the pocket to pocket dimension recorded earlier is needed. Adjust the placement of each new layout line that was transferred from the back, make sure the distance is that of the dimension that was recorded on the rail. This is hard to explain. Once the last set of layout lines is drawn it is ready to cut. Saw it a bit proud in the band saw and the use the sander to rough fit. Both rails are fitted the exact same way.
Then use long screws at the corner to secure.
Try in the opening, it will undoubtedly need some final fitting, simply remove the screws and with sanding blocks and files, remove small amounts in the joints where needed. It doesn't take much to square up, or remove a twist.
Then of course they are filled with tongue and groove or some sort of filler.
These take a bit of patience and practice, but they are not really all that difficult, or as difficult as my explanation would suggest

-Ron