Bricks, Masonry, Asphalt and Concrete - Bluestone foundation bulging repair or replace?

I am about to buy a circa 1900 Victorian with two bad bulges on a corner of the foundation of the house. The worst one is pushed out about 5 inches and has had a previous mortar patch which was successful. The stones are loose enough to be pulled out by hand right now if attempted. I am being told that the fix is to have a masonry contractor "push" the stones back into place and apply a better mortar and that this will hold. The estimate is $700. for this fix.

My unskilled and first reaction was that the whole section of wall should come out and be replaced and that would cost several thousand after jacking the house and removing the old and either pouring or building with block.

The dimensions of the main section of wall is roughly 14 ' x 7' although the bulge is primarily in one section of about 7x5. There is another section around the corner which is less dramatic but still bulging.

Main question: Can a fix be made by pushing the stones back into line and adding mortar that will be sucessful long term?

I need to make a decision on this real fast, any thoughts would be appreciated.

Thanks, Chris