"Personally, I think America was visited sporatically by many over the millennia."
There are many arguments for this but one of the most compelling is a note by the French explorer Sieur de La Salle in 1669 of an American Indian tribe on the north shore of Lake Huron. This tribe was uniformly light skinned, blue-eyed, and had red hair. Further intensifying the mystery La salle wrote that the red haired Indians had several words that he thought sounded Celtic. When La Salle returned to the region in 1672 the tribe had abandoned the area and were nowhere to be found.
This "lost tribe" pops up in comments by several other early explorers. The Jesuit Jacques Marquette was acting as a missionary among the Huron Indians in 1671 and met a red-headed captive of the Hurons that he initially mistook for a European. The Huron referred to the red-headed captive's people as the "fire haired people".
Pierre Esprit Radisson was a captive of the Iroquois and had a similar experience. Even Lewis and Clark refer to rumors of the light skinned people they heard when passing through what is now Yellowstone National Park.
Your arguments are some that I have read and convinced me that America has been visited regularly. Also, a tribe, I believe on Long Island, had a leader--a woman, whose name was Magnus. Not very Indian sounding! There were also rumors that some Indian tribes spoke, or at least understood, Welsh, which would seem to confirm that the Welsh prince--Maldoc?--did get to our shores with his boatloads of fellow Welsh. I've also read that there are documents in the Vatican archives that refer to priests sent here, or at least to an area that sounds like Northern US.
I still have two questions--which may not be very intelligent ones, which are: if Europeans got here, how come the wheel was not in use when later Europeans arrived? Of course, I'm assuming that the wheel was nowhere in use among NA Indians and I'm assuming that if a people were introduced to it, they would start to use it. Either may be incorrect assumptions. Two, wouldn't European contact have wiped out Natives from the diseases that later contact caused? I would think that oral history of such an event would have reached the ears of later European explorers. Just some thoughts.
Thanks for your post. This is a VERY interesting subject.