The authority of Congress in this matter is only limited by the Constitution (and amendments). The 14th amendment prohibits Congress from removing jus soli. Note the history of the 14th. It was added to expressly make it difficult for Congress to remove jus soli. As such, the 14th would work against #1.
As for scenario #2, yes. Congress can make it so that anyone is eligible to be President. That is, until, via the amendment process, a limitation is placed on Congress’s authority.
As for scenario #2 [Congress making everyone in the world natural born], yes. Congress can make it so that anyone is eligible to be President. That is, until, via the amendment process, a limitation is placed on Congress's authority.
Your interpretation would mean (before the 14th amendment and after the grandfathered generation passed) that Congress could have kept the presidency vacant by passing a law that defined everyone as "naturalized", and that Congress alternatively could (then and now) functionally eliminate the "natural born citizen" requirement by defining everyone in the world as a "natural born citizen" (of the U.S.).
I understand that you interpret the naturalization power broadly, but to me such extreme breadth makes no sense. Specifically, it makes no sense to me to suppose that the Constitution must or should be interpreted to give Congress such great power over the executive branch merely as a consequence of the specific grant to Congress of the power to make a uniform rule of naturalization.
The founders used the framework of specific enumerated powers to limit the authority of the central government. If each of the enumerated powers are interpreted so broadly as you advocate for the naturalization power, it seems the enumerated powers would have little or no limiting effect.