Like I said before, simply use a 1 1/2" by 3 or 4 foot metal strap and nail it in tension to the bottom of the joist. Don't worry too much about how close you get to the hole, except I wouldn't put a nail right through the center of the joist right where the hole is, and there's no point in putting one there anyway. Think of the strap as the rope in a tug of war, and nail appropriately. Also, like I said, placing a load bearing wall perpendicularly beneath the joist on the side of the hole where the joist spans the FARTHEST is helpful, and that's about as far as I would worry (at all) about this. Putting the wall directly underneath the hole in the joist is not helpful, unless you run the wall parallel to the joist itself.
Mostly, I wouldn't worry too much, based on what you've described.