What if Korean shipyards build the hulls with wiring and send them to American yards using sem-submersibles for furnishings?
I don't know if it is feasible, but I think it would be easier to just build the whole thing in Korea and / or Japan and ship the electronic components over to be installed. They could also have the Korean and Japanese yards compete for contracts.
The US yards could then focus of submarines, aircraft carries and repair work. Considering that they have limited resources in shipbuilding, something will have to change if they want to keep pace (or at least stay relevant) with China.
Again though, who knows how feasible any of that is? I don't even think the Pentagon is legally allowed to contract foreign countries to build ships. On top of the fact that you would be changing how many of these industrial institutions function on top of the optics of it all.