This appears to be field bindweed, or Convolvulus arvensis. It is a very difficult weed to control, and control efforts usually take several treatments over several seasons. For more information on integrated pest management practices for this weed, see http://ipm.ucanr.edu/PMG/PESTNOTES/pn7462.html
Yes, sorry to say, I think you are right. No easy fix for this one. I knew the roots were deep, but up to 20 feet - wow!
Thank you for your informative response.