“It’s a time-honored term to describe the multitude of islands, peoples, and things dotting the vast eastern Pacific.”
The “East Indies” is in SOUTH eastern Asia and nowhere near the migration routes of Asians to the Americas.
Define "nowhere near," and migration laughs. Migration is gradual, and it's a constant. The next village, the next island across that gulf, where there's better fishing, and pretty soon, a few hundred years later, some of your descendants are far away.
Notice that many Siberians have epicanthal folds. Notice that the Ainu of northern Japan and the Kamchatka Peninsula--who preceded the Japanese in Japan, etc., have both body hair like Westerners and epicanthal folds like the Japanese--who refer to the Ainu as "the Hairy Ainu."
When they studied the genotypes from both sides of the land bridge, they found plenty of "diversity." That should be no surprise. From the Philippines to Japan is the same distance as Japan to Siberia.