We have to admit we didn't solve this puzzle. I showed it to HitsMan who's a cacher in puzzle cache-free LA. He managed to figure out the missing bit of information and it all made sense.
We had been to this place for another cache long ago. Today there was a gathering not far from the cache location. I decided to decode the hint and try to go right to it to avoid people looking at me strangely. The hint was pretty precise and the location allowd me to conceal myself while I access the cache's unique container. TNLNSL. Thanks!