Long term strategy proposal:
Get the IoM to sublime, leaving behind splinter groups.
The IoM is a huge liability to almost every plan the Culture has. And they really have a duty to ethically remove it from play. Introducing sublimation technology and removing them in that manner, seems like the most ethically sound method of doing so. Sublimation is basically heaven, there would be no megadeaths, and no big resource sink for the Culture to take care of. The IoM doesn't really offer much to an ally, now that all of its interesting technology and knowledge has been taken(and the artefacts would remain behind anyway)

Frankly, Sublimation would appeal to other factions too, without any particular social engineering. The Eldar especially, and perhaps the Necrons.