My neighbor is now going through exactly the same situation it sounds like you are going through. His solutions is to trench down along the outside of the wall to the footings, put in drain pipe which he runs down to and then under the sidewalk and notch out the curb into the street, then with jacks and strong backs, push the 3' wall back and anchor it into the hill using some kind of anchoring system I haven't had the chance to figure out yet. But unlike yours, he has a very solid wall footing.
The trick to keeping a retaining will from leaning away from the hill it is there to retain is to have a deep and solid footing to support it, adequate mass and reinforcing structure to make it solid, but most importantly, a means for water that builds up behind it to get out. Best way is to make sure the wall has 'weep' holes along with a drainage pipe, backfilled with gravel around it, at the top of the footing, directing this low water away from the wall. If you are where it gets very cold, any water behind the wall when it gets below 28 degrees F will freeze and push the wall out, regardless of how strong it is.