I have been working up to this for many weeks, months, but I finally finished isolating the stump. By the end of August, I had expanded the trench to abut the stump on one side, and dug down deep enough to find the main roots.
The main roots spread out of the stump in all directions, but only in a fairly narrow range of depth. The roots cannot go down very far because the whole yard, including the tree, is sitting on a layer of rock. So the approach is to dig out all the top layer of dirt, which is pretty root free, until I hit root. Then clean the dirt off of the roots, and cut the roots off from the stump.
That lets us dig down into and thru the roots that underlie the stump until we are 9 to 12 inches into the rock, below anything of interest.
This is then repeated around the stump.
exposing more roots and more rocks.
Going around the stump both to the right and the left, isolates the stump more and more.
Continuing around the stump, we end up with two large root complexes. The irrigation pipe suggests this was at one point a "bubbler" which was meant to water the tree. The roots then grew towards the bubbler, and engulfed it.
Focusing on those two root complexes, we expanded the excavation area to find a thinner "other end" of them, cut those off, and then dug them out.
The first came in just a day.
But the second was much more trouble.
We dug down deeper around it.
And even tried to chisel out the stone underneath the root structure, until we were finally able to separate the stump from this batch of roots.
This leaves the stump, all by itself, sitting on a little pedestal of root.
10 weeks of work.