There are some flaws in the above.
ADA does not work with anyone, its a world in on itself, as in they are literally independent, hell DRDO labs feed it. HAL doesn't work with anyone either.
Sancho, what you are stating won't work specially because the way MoD has designed this structure, you need to understand they have choked any possibility of a nodal oversight and controlling agency under the PMO specifically because they will not give up their commanding position.
Its very difficult for me to put this in a post. Give me some time, I will collate the data for you.