So far most asteroid capture studies have started from the assumption that to be captured, an asteroid has to have a negative C3 with respect to Earth. This paper doesn't, and considers capturing asteroids into orbits that have positive C3 but are still somehow stuck close to Earth(deviation from a one year period are self-correcting) so that they remain in close proximity:http://arxiv.org/pdf/1501.03193v1.pdfMaybe something like this could be used to capture bigger/faster asteroids?
...Would a temporarily captured asteroid stick around a given neighborhood long enough for an ion engine to do the needed burn?