If this is as troublesome as it sounds, you may want to hire a "leak finder" service. What they do is purge your lines, then pressurize them with air and listen for leaks with a sonic-detection instrument and ear-phones. More typically used for underground leaks but I believe viable for hidden leaks in walls, too.

They're expensive...I would estimate a visit would be maybe 300 range. However, I can tell you from experience that they're good. They will pinpoint the leak location for you. May be worth a phone call if you're out of cheaper alternatives. At least they could explain what they do and allow you to consider.

I would also notify your insurance carrier. I suspect they'll help you. If so, they will cover this service as well.

" One at a time, turn on the valve to each water fixture and check to see if the meter starts turning. "

This is only useful if the leak is after the valve and is relatively large.

A very small leak may not have enough volume to measure on the meter in a short time, but when leaking 24 hours a day even a tiny drip can create a lot of damage.

The first place to start looking is the damage site and above.
Water still flows down hill though the path may not be very direct.