When I carry the bottle off road it usually stays in a pack, this is mostly traveling in and about cites and suburbs and the idea of keeping it a little hidden just keeps the strange looks from the locals and the LEO's from checking my bottle because I stand out from the norm even though all it has is water in it. Blending in with the crowd as much as possible is a plus, this set up is far better than my vertical set up, it just has noise.
People carrying water bottles of all types/styles are so common nowadays so I have a difficult time understanding your claims that locals and LEO's give you or your water bottle a strange look.
On the other hand, carrying the bottle in what at a first quick glance appears to be a "tactical" belt which holds the bottle in the small of your back then yes, people and especially LEO's will probably give you a strange/closer look which goes against your goal of blending in...
As for the sloshing, the sound is not going to travel very far especially against the normal noise backdrop of an urban background.
That said and as Hikermor already posted, carry the bottle upright and this will reduce the sloshing.
Another option is to create a baffle that can be inserted into the bottle. A PET bottle along with some creativity would make a good start to experiment with.