I dug back to the fence line along the right side of the electrical box, getting all of the stump and it's roots out. Going all the way down to bed-rock, I found the trench that runs along the fence (from the corner of the Bamboo Grove that holds the electrical, telephone and cable wiring.
Then I filled it back in, at least partially.
This has accomplished the basic goal for this section at this time -- removing the stump, clearing out the rocks, and making the soil better by increasing its organic content. I've mixed a lot of last Fall's leaves into this dirt as it was shovelled out, and then shovelled back in.
It appears that we will want to move the remaining trees. These are Shin Oaks -- a small native oak for Central Texas. It likes full sun, has low water requirements and likes the limestone based soil. So it's a nice tree, and we don't want to lose it, but it's sort of in an inconvenient place. My idea is to move it over to the corner of the yard.
So that will be the next area to dig. We will dig this area up, to get down to bedrock, clean out the rocks and improve the soil, then move the Shin Oaks over to that area and see if we can get them to live there. That will allow me to continue the excavations by the electrical box.
This area is where the compost pile was -- we've moved it now to back by the Bamboo Grove. Also we have had a couple of trees planted in this area, so the soil is somewhat disturbed and uneven; after the trees were put in or out, the soil settled. So part of the goal is to even up this part of the yard. We will need to be careful, since it will settle after we are done.