Firstly its possible to accept the mission without an empty S port, giving you no scanner but the mission to do. Pot luck in the terrorist ones, and hopeless in the CEO-finding ones...

Secondly, the defbots at a station fire at you on a terrorist mission if you tackle the terrorists too close to the station. One would hope they'd be a little more understanding...

Thirdly, the bot with the bomb tends to wingbug on the others blowing you all up and making standing plummet. This seems to reset itself upon relogging...

Another idea would be if you had low standing with a faction, you could accept a very high-risk mission to bring you back up to 0 (neutral) if you managed to do it but knock you down to -800 or lower if you failed.

Doing this for Itani when liked by Serco would reset both to 0, though, for instance.