Thank you for tackling this issue.
I agree with your proposed solution of adding rotated copies of the naval factory, but something should be done to avoid cluttering the build menu-just like others, I always found it weird how depending on whether you are on the right or left side of the map you'd have more or less problems (ships having to go around the factory itself).
You don't get this issue with ground or air factories as units are built in the middle of them, but any change here would most likely impact balance.