Except, the flaw there, is that the earliest signs of trans-oceanic, trans-island, seafaring capability of the Lapita Culture seems to go back to only 5000 or 6000 years ago, or so. FAR more recent than the Beringia migrations. You seem to be under the impression that Lapita seafaring is far older than there is is any evidence of it being. Where do you get this notion from?
The problem with Beringia is twofold: 1) when was the land above water, and 2) when was the land uncovered by ice. It's different at different times. Animals (e.g. the wolf) crossed around 170,000 years ago, and humans could have, too, but that's too early for most models. The last time the land bridge was open and had a habitable environment was around 12,000 years ago. The "bridge" is in fact a wide land that would have been open for thousands of years, not a sudden appearance.
The problem, as has been stated here, is that there's increasing evidence for humans in the Americas before then.
But as I've pointed out, people (e.g. the present-day Inuit) can live just fine in the Arctic without the land bridge, living primarily off of the sea. So humans don't need the land bridge to come over. Early models assumed that people didn't have good technologies for boat-related travel (even kayak or umiak - related travel) at that time, but that seems to be based just on unfounded assumptions. People acquire and lose technologies all the time; life isn't a game of Civilization.
So we can imagine a people in large kayaks, living on the edges of land deemed "unlivable" long before Beringia becomes habitable. Because their homes would have been places that are now covered by the sea, it's only natural that we wouldn't see them in the archaeological record. They might have moved over thousands of years from Taiwan to Japan, from Japan to Siberia, from Siberia to Alaska, from there to California, Mexico, and finally to Chile. Because moving inland would have meant changing lifeways from living off of the sea to hunting different things, the move down the coast would have been much faster than the move inland. Indeed, Chile is a great place for sea-faring people to make inland settlements, as one still needs the sea to live in Patagonia.
This theory is controversial right now, but is looking increasingly plausible. What we do know from genetics is that there were very few of them, and that they grew rapidly from a small population, and that there were multiple waves of migration from north to south.
What did they look like? That's a harder question. And, perhaps, an irrelevant one. The first arrivals - might have been a different population than later ones. We can even imagine around 40,000 years ago a population that takes to coastal waters, some of whom go south to Australia and some of whom go north, becoming Jomon, etc. And a later, Ainu-related population. And a later, Siberian population. But that's speculation.
Bear in mind this is not travel across open waters of the Pacific. But it doesn't make too much of a difference if people take twenty thousand years to go in a large arc around the Arctic and down North America or go straight across in a hundred. And the former is easier to believe. It isn't that much bigger of a distance, and you can do it slowly over thousands of years rather than in a few straight shots.
Travel across the open ocean is much, much harder and more risky, making this a fringe theory rather than one that people are open to speculation about. Academics don't like to dismiss theories out of hand (OK, aliens are out). Especially anthropologists, whose work is largely committed to challenging the racist assumptions of much of the rest of historical theory. But what I would want from a "directly across the sea" theory, and what is lacking right now, would be:
- introduced species in Polynesian islands.
- archaeological sites in Polynesian islands.