>If the year contained a February 29th, then they would be 1 year old and 2 days on the 1st of March...

So, they would be 1 year on Feb.28 and 1 year and 2 days on the 1st of March. They would never be 1 year and 1 day according this definition.

If we look from non-leap year into leap year, then I guess they would be 1 year 1 day on Feb. 29th, 1 year and 2 days on March 2. So here is no paradox.