Here's how it works: send a friendly PM to anyone able to take Junker missions, and if they agree to help you out then send a group invitation. You can be anywhere, it doesn't matter- the command is
/i playername
They will then take Junker missions- it doesn't matter that the Junkers hate you, they don't hate the other person and the game is nice enough to allow this kind of thing. Just trade or something until you have enough Junker rep to take missions (2 bars toward hostile). One thing to note is that while you are on a mission, tradelanes can only take you in the direction of the mission, with exception to the ones at each end which only go one way. This means that if you get lane hacked you either have to fly the rest of the way to the next hub, or go back and go in again. As in DO NOT GO TO NEWCASTLE WHILE HAVING REP-FIXES DONE.
Their is also the possibility of finding zoners who are working on their junker rep as well as we do a lot of adjustments to get different fations as neutral as possible.