I really can't say.  You should really have a check with this with Shadowfox. But I'd say you should just stick with the original Eldritch Knight concept.  Trying to replace the fighting style with magic initiate make the class strange and watered down from the start. Not to mention it seems to deviate from what it primarily is, a fighter.  Also why do you say they both sync at 3rd level?  The the original Eldritch Knight does not have Magic initiate unless feats are allowed.