Why not just allow there to be a NPC or quest involved to somehow merge the relic, mythic, and empyreal weapons together to combine the stats and maybe give a random augmented boost on the side? When doing this merging of the weapons though you have to specialize in the relic becoming a weapon only for one specific job though to do this. There should also be a cooldown period but after the cooldown period you can pry apart your merged weapons to make them individual again if you want to re-merge them or use them individually. With tweaked merged weapons and all combined WSs on one weapon that might solve everyone's issue of relic vs empyreal conflicts?

It's just an idea and might sound unbalanced, but I'm sure SE can figure out a way around that as well.