I am not going to wade into a discussion of Native American origins--my default position is always to lean toward the relevant scientific concensus (if there is one), but this isn't a field in which I have any expertise.
I do, however, have a serious question--and I ask this respectfully: why do you feel that accepting the theory of Asian origins would somehow diminish Native American identity and undermine Native claims to the land?
I live in Hawai'i, and about 20% of our people are (at least part) Native Hawaiian. We all know that their Polynesian ancestors came north, from Tahiti and the Marqueses archipelago, many centuries ago. But they were the first people to walk on these specks of volcanic soil, and as such they rightfully took possession of them. Centuries later, the United States wrongfully seized the islands during our brief but disastrous flirtation with 'manifest destiny.' None of that changes the fact that today the Hawaiians are acknowledged as our "host culture," and the majority of islanders recognize that the Hawaiians have suffered a massive injustice that still begs to be resolved. Why is it different for Native Americans?
I also have another, more personal example. For the past two thousand years, Jews--my people--have claimed to be (and have generally been accepted as) the descendents and heirs of the people memorialized in the Tanach (Bible). Now we have reason to believe however, that a substantial portion of the Khazari (who occupied a kingdom in eastern Europe, roughly where the Ukraine is today from about 650 C.E. to 965 C.E.) converted to Judaism, and may be the actual ancestors of many or most Ashkenazi Jews. Which means that I may have little or no DNA connecting me to the twelve tribes of Israel. But does that alter my understanding of myself as a Jew?
Not in the slightest. Again, because I do find this topic to be an interesting one, why and how is it different for Native Americans?