I have vascular TOS and it was very bad in the beginning. It was ATOS and when the blood flow slowed down, my heart would cramp. It was not recognized in the ER which was congruent with a later statement I read in a paper by a vascular MD that observed that TOS is underdiagnosed in the ER. It was not recognized by a cardiologist either. However, I finally got a diagnosis from Dr. Hugh Gelabert MD at UCLA as well as two chiros.
I have managed without surgery, but I have done a ton of self care, study, posture improvement, stretches, chiro and (appropriate) PT. It's like a part time job, although not as time consuming as it once was.
If you choose 1, you should expect to invest time in such activities. Or in other words, I don't think choice 1 in it's current form is any choice at all.
I think your choices are:
1. Conservative care of the kind described above until you feel you have improved, confirmed by another droppler US that shows even more bloodflow. Then stop warfarin.
3. Continue warfarin.
I have never studied the pros and cons of warfarin vs. surgery, so cannot comment on that.
The thing that stands out in your post is that (a) the doppler US shows improvement and (b) that is a relatively cheap test you can do again in the future after further conservative care. Right?
P.S. Don't sleep on that side. You'll compress the area.