Because I'm trying to get them to start a war with another faction, and if I understand the BGS correctly, then the famine has to end before a war can start. Unless that's incorrect.
Also, I already know about missions ending a famine state. Can I end a famine state without doing missions, and only selling commodities at a station that's not owned by the faction under famine? There's a reason I'm doing things a particular way, so I need that particular point cleared up.
That's incorrect, at least, slightly incorrect.
Only one state can be active at a time. *however* you can still get war queued up while the Famine is active, in fact, war will override the Famine (to paraphrase a dev, a starving population is one thing, but if that population were also fighting a war for their very survival, that would take precedence over trying to get food... no use eating if you're shot dead). So it shouldn't interfere with your ability to trigger war (unlike other conflict states, i.e if you're war pending in one system, you cannot get war/civil war/election pending in any other system until the conflict is over and cooldown expired). The BGS guide thread has more detail, but IIRC conflict states override all others, but cannot override other conflict states.
Ending the famine quickly without missions entirely depends on if the faction in famine has any station assets with commodities markets. If they do, you can sell food on the markets.
I can (probably) understand why you might not want to run missions to end the famine, if you're trying to queue a war you don't want to overshoot the target faction, but again that shouldn't be a problem when it's just a famine state. There's no real way to end the famine that doesn't cause an increase in influence to the faction in famine, except waiting for it to finish on it's own.