Well, going in line with FDev's MVP mantra, basic Carrier re-orientation could occur without a Bridge and via a Carrier Management Option in that very screen.
That would provide the most minimal effort conceivable - and rotating the thing slowly in that Management View should be quite doable.
It wouldn't be sexy - but mechanically get the job done for what it's worth.
Consider that they already had problems with the positioning system for carriers, and have noted they needed to fix this in some recent patch notes.
Now add the facing for this, which, apparently needs to happen in real time as well...
Nah.