Yeah, that’s one way to do it. Just remember the Epic Arcs can only be completed every 90 days so it’ll take a while to get high standings. Course on the other hand there’s very little to no negative derived standings incurred for completing the Epic Arcs.
Now if you don’t care about other Faction standings, then the fastest way to quickly gain Faction standing without having to do any combat missions at all is to just buy ‘Tags’ and complete missions for Data Center Agents.
However, if you want to gain positive standings with all Empire Factions then I suggest checking out ‘The Plan’.