If you use Howard Garrett's procedure, be sure that you only do it on odd-numbered Tuesdays in the second half of the month if the moon is full, standing on your left foot and reciting Walt Whitman poetry, wearing a blue colored shirt. It's all part of the miracle cure, but you have to do it exactly right.
Seriously... I understand the temptation to want to save the rose, and you might successfully do it. If the virus has spread throughout the plant (regardless of whether the mites are still there or not), it's systemically infected. On the other hand, a young infection may only affect one or a few canes; there's not much way to know for sure (but your case looks pretty advanced). Think about the risk/benefit before you decide for certain... you may risk the other roses in an effort to save this one. Consider carefully, and let us know how it goes. We're rooting for you either way.