QThe other day, I pulled my tee shot down the left side of a hole. When I found the ball, it was up against a thick hedge. I'm right-handed, so the only way to play the ball was to swing left-handed. When I addressed my ball with a lefty's stance, my feet were on an asphalt cart path. Did I deserve relief from the path? - Larry (Conway)
ARule 24-2b "Immovable Obstruction Relief" has an exception that, in part, says, "A player may not take relief under this Rule if interference by an immovable obstruction would occur only through use of an unnecessarily abnormal stance, swing, or direction of play." However, it sounds like your use of an abnormal stance was necessary in these circumstances. Therefore, you deserved relief for a left-handed stroke in accordance with Rule 24-2b(i).
Now, if you choose to take relief from the cart path, it's possible that the nearest point of relief could be in the middle of the hedge. Obviously, that's no good; so, you should probably examine your option(s) and make a decision before lifting the ball.
For what it's worth, Decision 24-2b/17 offers that after taking relief for a left-handed swing in this situation, you may then use a normal right-handed swing for your next stroke. If the obstruction interferes with the right-handed stroke, you may take relief again.