Yep! I'm going insane. I don't understand how to fix this.

Okay, I fixed it. Here's how I did it: For each affected contact (I only had one, so I have no idea if multiple contacts present different problems): (0) Have Messages open, but have the active conversation be one of your working contacts, NOT one of your broken contacts (not sure if this matters, but this is what I did). (1) Open something in Preview (an image, pdf, whatever). (2) Click the sharing button (box with an up-arrow coming out of it). (3) Select Messages (4) Enter the contact's name (duh) (5) Enter some text in the provided box (6) Send (7) Check your Messages conversations that were broken. (8) Rejoice