Another great topic for discussion.
First of, let's admit that some aspects of the production are not realistic. Even ground forces. On a large map, I produce enough SFTypes to field three divisions/turn. Or one armored division/turn. While one conceivably turn that material out in the two weeks of a turn, it wouldn't be possible to muster the troops and train them. And, to some degree it can be thought of as just throwing them out there green with no training, which is more or less what happens.
And, it is just as unrealistic to build a viable tank factory in just two weeks. One way of looking at it is the cost in PP, EP, etc., are part of the process. So, I am less worried about the realism of a shipyard being built in two weeks, and this can be controlled somewhat by the EP and PP needed.
But, building ships is more complicated beast. I am aware of the Liberty ships, and this could be easily modeled by a tech that makes them cheaper. But, some ships take a long time and they just can't be sped up. For example, the USS New Jersey: the keel was laid on 16 September 1940. It was launched on 7 December 1940, and was commissioned on 23 May 1943. It took 2 years and 8 months to be ready for sea duty. Possibly, it could have been sped up due to war time conditions (since it was started more than one year before the war started), but still it is a significant investment in production and material. So, how to model this realistically? And, there is a separate problem of setting things up generically for human vs AI (we'll get to this later). I think that naval production is something that will involve shipyards and changes to the ATG engine. It would seem to me that a model would be that a given line can ONLY have so much production. But, perhaps we would need to have a shipyard with multiple lines all with that maximum production. To be more realistic, there would also be need to be "large" shipyards. A shipyard where only large capital ships can be built. As not all shipyards can build battleships and carriers. The size, or type, can be done already, but not the lines. And, we can't "stack" LocTypes in a hex.
Another problem to keep in mind is raw. The raw requirement for the build is not "charged" until the unit is produced. So, the player has to keep this in mind while building ships. You could get to 100% production but not receive the ship until you have enough raw in your inventory.
What would probably best to do within the context of the current engine is to have shipyards with different production types able to make specific types. The production would be set up to give a "realistic" delivery for a single ship on one line using 100% production. You can split this if you like. Not 100% optimal, and the card is an idea that could work, but it will be complicated to pull off.
Also, I would make it that ships cannot be built at cities. Otherwise, it is a way around this.
As for the AI. This is a bit of a mess, and I am not sure that there is a good solution, or one without a LOT of work. In general, I don't allow shipyards to be a buildable LocType because there is a general unfairness when playing against the AI. It is difficult to place them. It is also difficult to make an event that would be guaranteed to be useful; that is not a shipyard on a small lake in the boonies (there is a way that I can think of but it would be a bit complex and would require some significant time at start).
I can see that I should also make a modification so that for games with only human players, some LocTypes can be built.