“Neither one would be eligible because Biden was chosen by Obama and elected as part of a team,”
Have you read the Constitution lately? If BO were to resign then Biden would become President. Pelosi would then become Vice President until Biden had appointed someone.
Pelosi would not become VP unless Biden nominated her and both houses of Congress voted to confirm the nomination. In the meantime the office of vice president would be vacant (as it was many times in our history before the 25th amendment was adopted—three times it was vacant for a space of 3 years and 11 months).
There has been a back and forth discussion regarding the matter which still hasn’t been resolved as Biden, himself, wasn’t elected on his own but as part of the Obama/Biden ticket and if Obama was not eligible then Biden wasn’t either since Obama chose Biden to be his running mate.