Not sure what you're expecting the vinegar to do. Soap greatly reduces the surface tension of water (so it doesn't "roll off") and will let any little leak create more visible soap bubbles. But, as others have said, if you're not seeing any bubbles then keep inflating the tube some more. I've sometimes inflated the tube until it's about 6' in diameter and several inches in width - that made the leak much easier to find.

Or - go ahead and use the 80mm stem - much better to have a tube with an 80mm stem that holds air than a tube with the right length that leaks. Edit: I see you did this - good. Now get some spare tubes with the valve length and type you prefer.

Or - pump up the current tube and go ride to the nearest store that'll sell you a tube. There must be a Target/X-Mart/etc. somewhere not too far away.