Hey,
I am not familiar with "ashtanga" or "downward dog", but I can tell ya my experience with labrum repairs. I'm a 25 year old male with a background in basketball and weight lifting. In November 2014, I tore BOTH of my labrums pretty darn bad. It was a kinda out of the blue thing, pushing my body too far and barely sleeping due to work and school. Okay, so I got surgery on them both. In January 2015 I got the left scoped, it was a 270 degree(3/4 torn) tear, requiring six anchors with zero bicep involvement and otherwise my shoulder was "absolutely pristine" straight from the surgeons mouth. This one was torn ballpark 3:30 to 12 o clock. I then in July 2015 got the right scoped and it was 180 degrees(1/2 torn) torn. That one required six anchors and was practically torn from I believe 3:30 to 10 o clock on the right shoulder. I am 6'7" and 225 lbs...
2015 was absolutely awful and I often thought I could never do this or that again, I really truly know where you're coming from. You're wrong, completely wrong. My left took soooo long to feel okay and ached daily even through my right's recovery, PT helped, yeah, but I actually didn't feel "exponentially better" until I was cleared to lift weights again and the majority of me finds this was more from depression and less from muscling the arm back up. I read everywhere, literally any labrum post on the interwebs I read. I was certain my days of dumbbell overhead press, weighted dips, and benching were done. They weren't and aren't. It took until about Feb 2016 until I wasn't afraid to do anything and I needed every bit of time to recover, but you'll be back to doing every pose you can imagine in Yoga...or whatever it is you guys do haha. If throwing 90 lb dumbbells over your head after 12 anchors are placed into your shoulders with zero pain whatsoever isn't gonna hurt me, you're gonna be just fine. Give it time and recover, know that you'll have long periods of frustration. I am stronger than before and I am a power lifter. I do not worry about ever hurting mine again in my sport.
Best,
Mike