there's a possibility that the water spots aren't spots at all, but rather
the glass has become etched from dried salt.

I didn't know that salt would etch glass, but maybe the glass is etched, in
which case there is nothing you can "remove" from the glass to make it look
clean. If the vinegar doesn't remove any residue, then try waxing it with
rain-x to fill in the etching. Would a razor blade remove anything?