I've seen this done with a bench foundation. You don't need to touch the existing foundation. You dig to the bottom of the continuous footing
and then down at a 45 degree angle away from the wall to the desired depth where your slab will sit. I'll find a pic. You will have a ledge either way at the perimeter but underpinning will get you more square footage than a bench foundation. It's probably more expensive due to the labor of digging every other 2 ft out under the footer and then infilling that w/ conc. and then going back and digging out between the new footings.
You should probably figure in at least a grand for structural engineer and the permit process as well.
7 ft is the min. height for a habitable room in the 2009 bldg. code. I think some cities/ townships want egress from the basement so you might want
to look into that more. A large window in the basement with a large window well looks pretty nice and could meet the egress requirement.
"Believing is seeing" - paraphrased from PH