Challenge: High Kings of the Chesepeake

The topic about St. Brendan leading to Irish colonization of North America got me thinking (and inspired an entry into my AH idea file with this topic).

How can we get it so when the European colonists arrive in North America, they find a hybrid Celtic-Amerindian civilization, complete with High Kings and the like, along the US East Coast?

Bonus points if this society has got bad memories of the English (aka were arriving as late as the Norman invasion of Ireland).

I've got some ideas already, but I was wondering what y'all thought.
 
I was going to use this idea on my Khazar timeline, and will incorporate it should I ever resume working on it. Basically my idea was that there is a greater Norse immigration onto Britain, leading to a Gaelic / Irish exodus which preempts the Norse settlement of Iceland. The Irish population grows for a century or two, and reaches the limit that Iceland could sustain. They then begin to colonize North America, and it goes from there.
 
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