This is just BS from journalistic ignorance.
India already had ICBM capabilities about 20 or so years ago when they launched their satellite launch vehicles. Probably decades before that. All they need to do is change the coat of paint on it to make it look more military and less civilian.
The only thing forcing India from a formal announcement of a globe-covering ICBM is political sensitivity. An ICBM in India’s arsenal that can cover the globe will only mean a threat for America, and Europe. India is not interested in sending such a message; neither does it need to do so. Both are the least of India’s threats.
For China, 3500 or so kms of range is more than enough.
India is separated from China by some of the highest and densest mountain ranges in the world. I think a more immediate concern, for India, is Tehran and Islamabad. And I cheer at the thought of Indian nuclear-armed submarine cruising the waters near those two capitals. We need India as an ally.
Range is always a factor of payload. As the range issues you discussed are logical, I think the better question to ask is, what are the Indians planning on putting on top of those China bound ICBMs that is so much heavier?