Scott:

This area of rough concrete that's 12 feet long by 6 feet wide...

1.) is the concrete in that area lower then the rest of the floor, higher than the rest of the floor, or about level with the rest of the floor but very much rougher than the rest of the floor?

2.) Is it in the middle of the floor, near one side of the floor or in a corner?

Could you not simply set a laser level on your basement floor and mark the spots on the concrete block foundation wall where the laser dot was. Then lower the mark by 1/4 to 1/2 inch to mark the level of the basement floor on the concrete block wall. Now, finally raise each of the marks on the concrete block wall by 1 5/8 inches. Now, use Tapcon screws to fasten a 2X4 to the concrete block wall so that the top of the 2X2 is even with that final set of marks.

Now, pick out a straight 2X4 at the lumber yard and cut a 1 5/8 inch notch ot of one corner. When you rest the notched end of the stud on the 2X2, the bottom of the stud will be level and even with the basement floor.

Now just paint the surface of the old concrete you want the new concrete to stick to with an concrete bonding agent and an old brush, and then let it dry.

Now, within the time period specified by the manufacturer of the conrete bonding agent, have a helper mix up some concrete mix and throw it with a shovel onto any areas that need to be a bit thicker. You just keep working that screed to ensure that all the concrete remaining behind the screed is level eith the bottom of the notched 2X4.

Then, cover the concrete with plastic while it cures to get it to cure as hard as possible, and then remove your 2X2 from the wall.

Bags of concrete mix will indicate how thick a pour you can do with the mix in that bag. Typically each bag will render 1/2 cubic foot of concrete, but the thinnest layer of concrete you could apply using that mix might be 3/4 inch thick because the largest size stones in the concrete are about 3/4 inch in diameter.

Some concrete mixes have fiberglass strands in them that hold the cured concrete together so that it doesn't crack. I know the fiberglass reinforced concrete is more expensive, but it'd use it for a relatively small repair like this one.