After waking up every sleep cycle and not settling for several night in a row, Elijah's nighttime behaviour is starting to drive us to distraction. Last night we tried a different tactic and went to settle him at the first sign of his waking. I'm not sure if it has helped, but it has definitely made us less frustrated, as he goes back to sleep without fully waking. So far tonight, he has not required a resettle after 2.5 hours, so maybe it did help. Or maybe he's just going back to some kind of normality.
Anyway, I've now bought "The No-Cry Sleep Solution" by Elizabeth Pantley and "Sleeping Like A Baby" by Pinky McKay (although, I worry a little about the name "Pinky" as I associate this name with the very eccentric Pinky Beecroft) as I did not want to do any kind of variation on controlled crying. I will be reading these books thoroughly, in the hope that something will give me a light bulb moment.