Phantom Text Messages — They won't go away, even when I've read them!

For two months now my Messages app on my iPhone has shown 32 unread text messages in the notifications badge. All of the offending messages are from the same person (my partner, with whom I text frequently). Additionally, when I try to text that person, sometimes my new messages will not go through — they'll get held up in "Sending" for ages, or simply show up as not delivered.

I've tried everything. I've quit Messages. I've turned notifications off and on. I've reset the network, I've reset all settings. I've tried deleting a few messages from the conversation and restarting and I've tried deleting the entire conversation. I've asked Siri to "read unread messages," which has her read aloud all 32 of those messages (all of which are from when we were traveling in Europe in May), a humorous enterprise which still doesn't remove the "32 unread messages" notification. I've erased and restored the entire phone from an iCloud backup.

At this point I have no idea what to do! I may try to erase the entire phone and reinstall all the aspects individually, though I'd be sad to lose all of my text messages. There's a lot of history there, and I frequently search through old messages for work-related information. (A lot of my work is indexed in Messages.)

Does anyone have a fix? Or at the very least a way to archive my old Messages so I can go through them later?

thanks,

DV