1) It's sad that we need this. However, I've talked to many, many customers that are not at all shy about being openly racist, and as long as we continue to entertain that "The customer is always right" mentality, it won't go away. I had customers who would get very hostile with my coworker adjacent to my desk who was from Pakistan but lived in the US, and often the customer would not believe that he was in the US until I audibly walked over to his desk and said in my loudest white-guy mid-Atlantic accent, "Hey, Mohammad! What seems to be the problem?"
2) I don't think this approach will work, if for no other reason than that Indian-British English has a distinctive style to it that extends beyond the accent. I once took a Udemy course (might've been on Elasticsearch?) and it was very clearly written by someone in India who then paid a white guy to read all of the slides in his American English accent. The results were hilarious, because the guy was clearly trying to do his best to make "do the needful" sound like something a Bay Area dude would naturally say, but, it simply wasn't.
3) For what it's worth, while I can immediately tell when I've called into a tech call-center based in India, I've been genuinely surprised at the relative lack of "foreign accent" when I've called into a call-center based out of Singapore or the Philippines. To my ears it sounded like non-distinct English (e.g. not quite American but not quite British either, and certainly not Indian).