That’s an interesting conundrum and one that I’ve not encountered before as a coach. It seems to me that re-teeing is the only real choice here. I’m interested in #3, though. Since there is no limit to how far back along the line you can go, is it not possible to go back far enough to get behind the briars? You might be in another nasty position, but that’s the breaks.
Also, not seeing the actual place, I wonder if there is not a swath of grass or dirt between the briars and the bunker. If so, you could take your drop on that strip two clublengths away from the hole—this might be possible if you ran the clublength parallel to and between the bunker and briars.. If you dropped it twice and both times it rolled into the hazard on the third, you could PLACE the ball on the spot where it contacted (I haven’t looked that two drop-three place rule up, so it might be three drop). Of course, this might mean that you would be hitting the ball left handed with your feet in the bunker, but that’s legit.
Finally, I’m wondering what sort of a sadist designed that hole