I have smaller problem but same persistance here in NM.
I've been getting a bit ahead on eradication by spraying areas with supe concentrated vinegar.
The plants take it in - we are so dry- might not be as 'easy' if you get rain often.
Anyway seems to knock out much but is still year 4 of trials year 2 post spray- but much better than trying to pull all. which of course is not any fun.
One little notch left behind and it becomes an undrground monster in 2 seasons!
Anyway I went to Cedarcide and bought the super concentrated vinegar for this and for some
cleaning- not too toxic or at all when diluted by rain or rinse.