OTOH, it is also possible (and very easy) to subvert the AICivs' MPPs with each other. MPPs are activated by overt acts of war -- killing invaders on your own territory is considered justifiable, but invading, bombarding or capturing units on foreign territory is not. (I'm not sure about attacks on neutral territory, but probably best not to risk it). So if you want to attack someone, as long as you are confident that you can afford to risk playing the 'victim' for 1 turn, all you have to do is trick your will-be-enemy into being the aggressor. The AICivs are usually quite ready to be tricked.
The way you do this is, you sign MPPs with all the Civs that they have them with -- or at least, with the 2-3 most powerful of those Civs -- then declare war on them, but don't attack yet. To minimise your losses, make sure that any potentially vulnerable border cities are well defended (put all your mil-units in them, if necessary) before you hit 'End Turn'. This will encourage your target to bypass those cities and send its units deeper into your territory. Leaving a cheap 'bait' unit (e.g. a Worker) on/near your border is also a surefire way to get an AICiv to attack where you want them to. (BTW, you do also have lots of Arty, and rails to move them around on, don't you...?)
As soon as your enemy commits an act of war against you, all their Mutual Protectors will declare on them, breaking their MPPs (and any other active trade deals). You can then also sign Alliances if you wish, but this is not necessary, and may actually be counterproductive if all you want is a short war to grab a resource or two -- signing an MA commits you to a 20T-deal, so you can't sign a Peace Treaty with your enemy before that time is up, or your trade-rep will be toast (so if you don't want to fight for 20T, you'd better just hope that your allies sign PTs first).
Hey presto, you are now at war, and because all the MPPs have activated in your favour, you are now also free to go rampaging across your enemy's land.