My response to yours is:
- India knows all it is likely able to do is to delay CPEC and make it more expensive on time, money, and resources. The end is the same, and CPEC will be successfully implemented, no matter how much hassle New Delhi causes
- India knows it's probably better off being inside CPEC, where it can affect some policies to better suit its interests, and also to keep a closer eye on its rivals
- India joined the AIIB, even though it was suspicious of Chinese dominance in the bank, so CPEC wouldn't be the first China-sponsored project it joins
- India is part of the BRICS and a member of the BRICS Development Bank, so it already has dealings with China in a multi-lateral economic enterprise
- Beijing's history and modus operandi is inclusion, and there are no good reasons to expect it to behave differently vis-a-vis CPEC
If that's so, then you'll need to explain why India would be less suspicious of China as partner in the China-lead BRI than the China-lead CPEC.
Taking your message at face value, it argues for China to put its best diplomats on getting India aboard the CPEC train, while at the same time reassure Pakistan it is still China's special friend. The reason is because, on balance, it's in everyone's interests to have a satiated India than an aggrieved one. Plus, the cake is big enough for everyone to have a piece.
CPEC by its very nature is going to benefit Pakistan much more than India. The India-Pakistan border is basically desert plus disputed border areas, which limits opportunities at this time.
Plus India is always going to feel ganged up upon because it will frequently be 2 versus 1.
So inviting India to CPEC is a stretch too far at this point.
---
India joined the AIIB, because China has voluntarily submitted itself to a common set of rules and limited its voting rights in the organisation. There are a lot of voices in AIIB.
BRICs Bank is the same, where there are other voices at the table.
India will have to be dealt with specially, precisely because it is much bigger than anyone else in region, and holds a geographically central position in OBOR
So a 1 on 1 forum between China-India is required, not least to satisfy India's sense of place. And the plans discussed at this forum would naturally focus on Indian development/connectivity. BCIM is probably the first step because the closest part of populated China is Yunnan province which borders Myanmar, and can serve as a neutral buffer state between China and India, to allay Indian suspicions on direct connectivity.
Note that India has an automatic suspicion of anything Chinese because the media portrays China as being aggressive/nefarious and launching the Sino-Indian war
But the crazy thing is that the Times of India published a special report a few years ago, saying that the still classified Henderson-Brooks report actually places most of the blame on India for starting a war that it knew it couldn't win and which was incompetently run when it started.
So yes, China does need to make a special effort with India given the situation, but a rational India should recognise that it is in its best interests to work more closely with China.
However, the main issue is that the Indian government is not noted for being particularly rational or competent, so it will take time.