I-Beams are a very effective repair. We have been installing them for over fifty years. If we determine beams to be the fitting repair, you can have confidence that your foundation is sound.
In all the years we have been installing them, we have removed many beams installed from other companies. They were either too small, too far apart, or attached incorrectly. We provide a lifetime warranty on these beams, and we have never had to return to repair a single beam.
The new technique used by others is to attempt to push the wall back into place by installing a bolt at the top of the brace. While this proves to be effective from time to time in the right conditions, it uses the floor joists as leverage and can cause damage. Floor joist can snap and blocks can crack.
The safest way to push a wall back once damaged is by excavating the wall from the outside, push the wall back into place, and then stabilize the wall with bracing.