Would the game be simpler if in addition to the term Ships (fighters, destroyers, cruisers, carriers, dreadnoughts and Warsuns) there was the term Starships (destroyers, cruisers, carriers, dreadnoughts and Warsuns), instead of the clumsy term (imho) non fighter ships?

That way Master of Ships would be I control Meccatol Rex, and have a spacedock and 8 starships there.

I suppose there is no rule against doing so. Simply call it a house rule and run with it.