I conjecture that it would make for an interesting media project like the Abramsverse, but with the sheer amount of cruelty and killing that the Terran Empire entails, how could it live up to Gene Roddenberry's legacy?
Easy. Only the heroes need to be examples of virtue fighting against the evil empire, e.g. exchange the crew but keep the cool mirror styles (Excelsior: Shattered Universe
), have them survive against the mighty empire and feature trigger-happy but ultimately honorable Klingon warriors you earn as allies (cf. ENT "The Andorian Incident", Vulcan-Andorian arc) and overthrow/reform the evil Terran Empire in the third movie (cf. Star Wars, Rise Like Lions