I wish that I had better news...
It seems to be the case that warranties in India are ALLOWED by Law to only be honored at the PLACE of Purchase - the actual STORE - even if you bought an Apple product across the street in Mumbai, an Apple Authorized Reseller/Service Provider could refuse to honor the warranty
That said, even if AppleCare+ = an EXTENDED Warranty policy = was valid in countries other than its purchase (it isn't, simply because it is a legal contract that must be adjudicated under the set of laws under which it was executed/bought), it was run afoul of this wacky policy
A respected member here, the late seventy one, familiar with doing all kinds of business in India called it "The Wild West"
Apple has been looking for ways to find it possible from a business standpoint to do business under Apple control for years - but India's laws require that ALL businesses be majority owned by an Indian entity - and Apple doesn't do partners, much less majority ones
I am unsure how you would go about cancelling the Singapore AppleCare+ policy. You may not want to since you will have to return to Singapore to get warranty service anyway.
It MAY be possible to find some ROGUE Apple Service Provider that actually HONORS Apple warranties - but that is a long shot
Apple does have a wholly owned subsidiary to handle what operations it does have
How to Contact Us - Apple (INDIA)
I would post the phone number from the top right of that page, but there is a filter running here that prevents most if not all Indian phone numbers from posting due to anti-SPAM efforts
Like Allan said, we here are all user volunteers so what we post is merely reporting what we have learned from participating here, not official Apple policy