Hi Rob,
Sorry there's not much that I can advise because I gave up. My plan was to do exactly what you did, but then I got a different idea. My MacBook also had a faulty keyboard which was eligible for free official Apple repair. So I brought it to authorised service for keyboard replacement with a slight hope that they would also fix the screen. But an hour later, I got a message from them that the MacBook has liquid damage and therefore is no eligible for ANY free repair. It sounded like BS to me because I've never spilled anything on the Mac, but they sent me pictures which did look like liquid damage. Also, they pointed out that the battery was swollen and replacing it would also cost a good deal of money. Overall, to get everything fixed, they quoted more than the original machine cost me 3.5 years ago when it was new!
I also checked with unofficial Apple service - they quoted about half of the price but it was still ridiculous amount of money. It was not worth it to repair such a badly designed laptop. As you say, the screen issue would have reappeared anyway at some stage. I ended up selling it to a second hand shop for parts. They gave me €400 and I bought a used Unibody MacBook Pro for half of that. Not a suitable solution for a professional but it's surprisingly good for the usual stuff like browsing, movies, YouTube, some coding etc.