Dropping INF is hard - much harder than rising it. Two more possibilities for you:
- take on passenger missions from the faction you want to drop, and then fail them (e.g. by getting your ship, with the passengers on board, destroyed. You don't even have to leave the station). Downside is that this also hurts your REP, and you won't get any more missions from them after a little while. So you need to find another system with that faction and do some REP work there, then return and continue with lowering their INF
- the overall INF in a system is always fixed to 100%. So instead of targeting to lower the INF of one faction, you can raise the INF of (ideally all) others.
