I think concrete bits and powdered concrete from the removal could raise pH.
I think what must be firmly compacted soil base would be a problem. Can you at least fracture that -- you don't have to dig up
, just break
Here is a link to another member's success with a broadfork
Subject: How to break up rock-hard soil?
I have a tool called digging bar
it is very heavy -- mine has a point on one end and a 3" wide flat "spade" on the other end. I use the pointed end to easily make 12-18" deep "pilot holes" for fence posts, but instead of pulling straight back up, you could use this like a lever to fracture soil.
Once the soil is fractured, you could spread compost or composted manure which will be washed down the channels made by fracturing. And the soil microbes and attracted earthworms, as well as plant roots will follow them down, If you are not planting right away you can use unfinished compost (if you have any) or incompletely aged manure which would be more biologically active -- but then you'd have to wait for 2-3 months.
6-8" is rather shallow so it will dictate plant choices. That and the pH issue. What were you thinking of planting? It's actually better to plant a more pioneering type deep rooted plants with less than ideal performance this first planting because the roots will help to break up and integrate organic matter into the subsoil.