Dear Sir,
This is a very interesting and insightful set of points as to why an incarnation can only come in Hinduism.
I have a different perception, and that is, that all religions have their origin in God, and so the road is not closed off to a God-Incarnation in any religion. What matters is not the religion itself, but the level of spiritual development of the individual persons. The God-Incarnation can only take place amongst a people where the inner spiritual development is highest. Outwardly they may follow any other religion, but inwardly, they may already be mature from previous lives.
Many people see India as a spiritually advanced society. But when we look at India today, we hardly find spiritual advancement. Can an Avatar come amongst a people where there is so much corruption, not just at the level of the political leadership, but at pretty much every level of society? Also, in a people where there is either on the one hand mass superstition or on the other a complete intellectual attitude which only focuses on studying well and succeeding materially? The level of maturity of the people is also therefore important.
In the course of my spiritual search, I have come to see that there is no one single race or religion today that is spiritually mature for an Incarnation to take place. But I am sure at one time earlier, there was a people that was mature enough for this Incarnation. Whoever they were, it is naturally not possible to provide "scientific proof".
I am perhaps not explaining this correctly. I know a book entitled "From India to the Truth", which is available on the website
www.sphatik.net, and that goes into greater details on subjects like these. It is worth obtaining and delving into.
Thank you again for your insightful comment, sir.