"I believe the discussion now is shifting to what is the most libertarian theory of property? Is it the labor theory of property, as Locke and Rothbard thought, or is the first occupier theory, as Kinsella claims?"
Locke, Kinsella, and Rothbard all believe in the Homestead Principle, which states that the first person to make use of unowned resources is the rightful owner.
For example: A farmer homesteads previously unowned land when he becomes the first person to plow it and plant it, and gains rightful ownership of it.
There is no conflict here.
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"The State is a gang of thieves writ large." - Murray Rothbard