Ok...
I had the same problem. Here is what happened:
I tried everything except for asking Siri to "read my unread text messages". Being unable to solve the issue and seeing message numbers increasing, I decided to give it a try.
Tip: Try turning on "type to siri" because after reading messages, Siri asks if you want a reply, sometimes, even if I yelled "Nooo!" it did not detect, but typing no always worked.
Anyway, with a little patience, I managed to get the unread msg counter down by about 200 (took half an hour, as Siri read spam sms messages from the same sender in a chain).
Seeing that it worked, I decided to do this whenever I had the time.
But...suddenly, after Siri read about 200 msg, today several hundred messages in like 20-30 conversations "reappeared" and I deleted most of them manually.
There are still 85 invisible messages hiding somewhere, but I am sure Siri will find and read them or they will re-appear after Siri locates conversations.
This is how it worked for me...
Also I would like to report this to Apple Admins here as this seems to me as a bug that needs to be addressed.
Hope it is helpfull...