So, the year is 1945. WWII has just ended, the dust has settled, and India demands independence from the Empire; but the exact form which it will take is still very much up for debate. How would AH.com handle it?
I'd do what happened in Iraq and Egypt, and install a puppet king over all of the British Raj, and formally no British people will serve the king. The king will proclaim himself a reincarnation of a Hindu deity and the governor of the Caliphate in India (or something like that). When the inevitable happens and Britain must withdraw its empire, it can be done in a face saving manner. Eventually the king gets overthrown like the Egyptian and Iraqi ones, or he muddles through like the Jordanian one.
I think they would settle for the states of North and South Dakota and probably give them Arizona and New Mexico.
What reserect the Mughal Emperors? Could be interesting, would George VI have to 'adopt' a Mughal to be in-line for the Indian throne though?
That would be too obvious. I would proclaim a new dynasty whose royal family would be from a princely state who would cause the least trouble among the public. The new dynasty would rule all of the British Raj and would consciously use Indian and Hindu symbols, and appoint as many (British-educated) Indian nationalists as bureaucrats as possible. But behind the scenes Britain retains a degree of influence. Over the next 20 years the British "advisors" would gradually be withdrawn until the Indian dynasty is genuinely independent, though with an Anglophile elite. Britain takes credit for a peaceful and orderly transition while ensuring its political interests are left intact.
By 1920, it's not inconceivable for India to be a dominion, that would lead to it eventually becoming fully independent by 1947, but united. Without Gandhi, you'll see a huge boost in a united India, since he brought in spiritualism into the movement.1920 is too early; the Indians who desire independence are not sufficiently organized to form a government if the British leave. In 1939 tensions in Europe are running high, especially after Germany occupies Czechosloviaka in March. The British are not going to be willing to give India up then, not when they need their help.
1945 is a little early, but not excessively so. Given the situation we would probably go with the OTL solution of dividing it into Pakistan, India, and Bangladesh. Kashmir should probably be divided between India and Pakistan, but getting them to agree on a particular division would be difficult at best; it would have to be something set by international treaty, like the 38th parallel line between the Koreas.
I think they would settle for the states of North and South Dakota and probably give them Arizona and New Mexico.