is there any way to get the actual Mist Repeller tech after completing the mission, other than stealing it at random or allying with Synedrion?
Nope. I just wait to be allied. They won’t have the usable tech researched for a while, but I don’t know if one steals enough research that it can be gotten earlier than when they research it.
AFAIK (I usually don’t steel tech):
You can only steal tech that they have researched yet. If there is no tech left to steal then you gain a lot of research points by accomplish the steel research mission.
You don’t have to be ALLIED (i.e. faction reputation 75%+) with Synedrion to get the Mist Repeller research from them.
Being ALIGNED (i.e. faction rep. 50%+) with a faction is enough to get ALL tech currently already researched by them shared with you, as well s as any new tech they will research while still aligned.