I'm fairly familiar with manzanita removal, but not sure of what your talking about. If it's similar, than it will come out real easy in winter when the ground is soft, but almost impossible when it's dry out.
A small dozer of the 80 to 100 hp range will work well at getting it out and pilling it up. Even better would be a trackhoe in the same HP range, or a backhoe will do it too. We used a backhoe to get it out and had good results in winter, but miserable in summer.
Never tried it with a thumb, but I think that would be the ideal method. Just pluck them out and pile them up for burning.
Good luck,
Eddie