I'm just trying to understand how insensitive it is to comment on a thread where OP is clearly someone who has either suffered loss or has an entire network suffering loss, and then go full strong systemiser and ask for a reference.
The absurdity of asking is even stronger when almost any understanding of the situation on the ground in India would mean an understanding that there is widespread and systemic problems with data collection in India, essentially as there has been throughout the pandemic globally, reflecting the difficulty of determining infection rates, CFR vs IFR and deaths in a testing scarcity environment.
I don't know for sure but I would anticipate that there is a good chance that many indian deaths are never registered which would make other post pandemic methods of determining true 'excess mortality' very difficult.
The particular irony in this whole post extending from your question being that the BBC itself, in the linked article, in the second paragraph, states that 'experts say the real death toll is several times higher'.
Now that isn't your 1-2 magnitudes but you don't have to travel far from there to get those types of sources, but depending on how strong-systemiser you go on requiring hard numbers, the fact is no-one will ever know because no one is counting