@ Nuke.
[thinking...] You know, that might actually work. You'd need a whole lot of noble gas for the ion thrusters, though. At first, I was thinking that the specific impulse of those things would be so small that it couldn't work, but thing is, you can keep them running for years on end so long as you can keep them supplied with reaction mass. Over those times scales, the change in momentum might be enough after all. I wonder if there's anything on Apophis itself that could be used in that capacity? Can ion thrusters be run of something other than xenon, neon, or other noble gases?
Not so sure about gyros, though. I mean, yeah, you could, I guess, but ye gads, those things would have to be spinning fast to make a dent on the spin of something that big. I think you'd be better off using ion (or other electric) drives for torque to stabilize the thing first, and then use gyros to keep it stable. Even in microgravity vacuum, there are material limits to how much RPM our bearings can handle!