You are right to keep trying. I've been an Apple customer for a long time. Generally, I've gotten superb customer service - both in the US and India.
1. Don't settle for a malfunctioning home button. I have had menu botton problems with my iphone twice. They only got worse. Apple very happily replaced both iphones (many years apart)
2. Keep trying. Ask for a supervisor. That tends to get things solved. One time, I had a supervisor who I thought was doing a really bad job and did not seem to understand my issue at all (itunes). After writing back and forth for weeks, I simply called and got a fresh start. (Itunes is only email support - but I called for tech support with downloading and then moved over to itunes) My problem was solved immediately and I was completely satisfied.
3. To all those who assume CR in India is bad, I think we should all check our assumptions. I've been disturbed for years by people inferring that people in India can't do the job. Why not? There are good and bad tech support reps in India and the US.