That very month, I had to fly to India for some work and I decided to ask a local authorized Apple service outlet. The guy changed the display for me at no charge. The machine was out of warranty by atleast a year at that point. But still, Apple honored that warranty.
Six months later, I got a blue tint on my display and the guy did another replacement free of cost because the replacement display he gave me was faulty.
I spent $0.
Many Apple service outlets are pretty good, especially in Asia - Singapore has some good outlets too apart from the one I went to, HK, China all have very knowledgeable people running these outlets too.
Here's another one - I currently own a Samsung S10 phone. One of the speakers became bleak and service center A refused to honor the warranty because the phone had "water damage". It is an IP68 water proof rated phone. How the fuck can it have water damage? Especially when the phone is working just fine, except for the top speaker being bleak.
Service center B did the job of speaker replacement in under 2 hours.
This is the reality. My point is, service centers are like any other business, some people are knowledgeable, some people are spiteful, some people are stupid.
So how do you figure out which ones are good and bad? My simple rule of thumb is ask around your extended family, usually they will know someone who they can refer you to. Referral based jobs are the best, since there is an element of personal touch involved. If not, scan for google reviews of the place to find the ratio of positive and negative reviews. Read the negative reviews especially as its a good indicator of the center's competence.