Nice tree
http://plantsdatabase.com/showpicture/12541/
From what I've read, improving the soil will improve the tree. I wonder what would happen if you sprayed the leaves with vinegar? I normally don't recommend using vinegar on anything but turf weeds, but this is a horse of a different color. It would involve using special equipment to get up there to spray.
Could you get up to a branch and girdle it to see what happens? I'd be afraid the roots would respond by sending out new shoots, but it might just start to cut back root production while the branch dies. Then girdle one branch at a time until they're all girdled and then you could girdle the tree trunk. You would have to keep after any shoots.
I wonder if any of the native deer, elk, sheep, or any other wildlife would eat the trees?
Or how about using a dozer to pull out the entire tree, roots and all? Or cut it off and use a stump grinder to take out the roots?