The problem is that India had a colossal (comparatively) population - roughly 300 million in 1800 - and these natives were aborigines or tribesmen but the citizens of long-established civilisations. The Indians were committed to an "advanced" religion (by "advanced" I again mean considering the numbers of tribesmen encountered who could be taught to see Christian practices as synonymous with their own more Pagan beliefs, etc), which they were not willing to abandon; they had social codes which they could not be persuaded to drop; they had culture and institutions which were too civilised or developed to be overwritten with English culture. Imagine, if you will, that say 20,000 people move to some part of the Eastern Seaboard of the USA tomorrow, and these people have a distinct culture and set of political and ethical values which they claim to be more advanced than our world currently knows. Will these 20,000 overwrite American culture? Well they might get a couple of ideas in, a few words adopted maybe, but by and large those 20,000 are going to have to adapt to American culture or by left by the wayside. Now for the British India situation, being outcasts from society is not an option as the Brits there are supposed to be the ruling class, or important merchants and such, and so they must be seen to interact with and be a part of society at large. So they are left with little choice - Europeans who went to India essentially became quite Indian, rather than vice versa. And there were actually quite a large number of Brits and other Europeans in India. Sending 500,000 Loyalists will probably no more than double the number of Europeans there, which is by no means a large enough influx to suggest a change in the balance of power - especially in some place as well-entrenched in its ways as India.
I've wondered a number of times on how this could be changed, and my main conclusion is that it would be very hard if possible at all. My current, though naturally flawed and incomplete, theory is to keep the percentage of the Indian land/population within the Princely States high - each of these states were generally on their own quite small and "quaint", and since the European powers dominated the coastlines they depended on the British for trade and contact with the outside world. Over time this gives you the chance to essentially make them reliant on the British for the importation of new cultural anomalies as culture changes over time - whereas a large Indian state such as the Mughal Empire or the Maratha Confederacy could generate its own cultural development, tiny petty states are unlikely to be successful in this, and thus are more likely to "follow the trends" that they see being practised elsewhere. Since each of the Princely State rulers were quite wealthy but little able to exercise their wealth alone, the rulers were generally quite receptive to British influence, too, thus allowing them if the British are able to so do to be inducted into British Indian High Society, which could provide a top-down impetus for adoption of certain traits. If you allow the native Indians to enter the ranks of the Civil Service a little earlier, too, you provide an incentive for the middle classes to consider themselves a part of the British machinery of state, a concept which was little able to develop before Indian received independence OTL. This, hopefully, will also encourage the disenfranchised lower classes to consider their ethnic countrymen to be both the bringer of social improvements, and the scapegoats for when things go wrong - in essence what this is doing is encouraging the average Indians to cast aside their views of the British as usurping all the power, instead apportioning equal blame for failures on their own countrymen (and thus slowly eroding the idea of the British as being solely responsible for all bad government in India) while forcing them to respect Indian government officials who respect and work with the British when things go well. What I essentially am proposing is that by setting up several and various methods of allowing British culture to trickle down through society then slowly the Indian masses could adopt a more Anglicised stance.