Sadly, Syntaur never replied to my availability/price inquiry for this part...
I finally decided to open it up to check how the inside is made, and it happens to be pretty simple: only a ribbon cable is connecting the LCD to the main board, without a connector! It's simply bare at both ends, and can be inserted in the right input. It's a little thin, but doesn't seem that fragile. The LCD is mounted on a TR-804 94V-0 PCB (also stamped TRULY MCG445-A1), but it's so small and compact it would most likely be impossible to troubleshoot and repair...
Now the only thing missing is the true knowledge that the problem is related only to the LCD part itself, and not elsewhere on the board...

I can't swap it with another one for a test, so even if I buy a new one I won't be sure until I plug it in.
Anyone can tell me if those lines can be a symptom of something else going bad BESIDE the LCD itself? I don't know anything about this.
[Yes, I have unplugged the ribbon connector on both ends to check for any visible defect.]