Yes, you are correct - thanks for pointing that out. That is an error, we are talking about DI (diabetes insipidus) NOT SIADH. They would have opposite effects and ME patients tend to have a mild version of the former.
Yes, you need to check the blood - urine osmolality should vary to keep blood constant, but in and of itself doesn't really matter. The (very old) test for DI was water deprivation for 12 hrs overnight and then looking at whether the urine was concentrated - it's not a bad place to start, as ME patients don't do that as well.
I don't have any of the nocturia symptoms at all really. I often don't sleep through the night, even with lots of pills for it, but I won't actually get up - it has nothing to do with urination, my brain just sucks at sleeping for long periods straight. It prefers to sleep whenever I need it to do something useful... I have had some really low ADH readings.
Too many NSAIDS can be bad for the kidneys btw - so watch out for that. They act by inhibiting cyclooxygenase, so prostaglandins are reduced - but prostaglandins have key roles in many systems in the body, including the kidneys and stomach. Nephrologists as a rule hate NSAIDS and tell their patients to never take them. Tylenol won't hurt kidneys, but it will screw up your liver... Not that these are always unsafe drugs, but as everything, in moderation. For kidneys, an aspirin a day doesn't seem to be a problem - although it anticoagulates you, so that's another risk (or benefit, depending on the circumstances).