Thanks for your advice by the way, Jmanis.
We have been able to trigger wars and elections pretty quickly by strictly not doing massacre missions at all for the system, only running high influence missions for the faction we want to increase, selling commodities at a loss at faction station we want to decrease and even allowing missions to run out for the faction too.
We must have triggered over 10 conflicts this way to the point we now have control of 5 of the 7 main stations in the system.
It's been hard work but well worth it. Thanks again.
PS. And to Goemon too.