What is a Michigan Basement? | Prugar Consulting, Inc.
My grandparent's house had a basement like this. There was a concrete shelf about 2-3 feet wide that went from the top of the actual basement block wall to the bottom of the original crawlspace foundation. The basement wall is set inside the original house perimeter.
Perhaps you could do something like that on the wall where the addition meets the existing house, and a regular poured or laid block wall for the other three addition basement walls.
Tying the two parts of the house together would depend on which direction the new floor joists run, parallel or perpendicular to the existing house floor. Parallel sounds easier. I assume your goal is same height floors in both parts.