God help us if it gets to Chao.
According to constitutional law scholars I spoke to on this subject (not the change of the sequence part but the citizenship of the persons in the lineup), the authority vested in the President would be in that persons hands, but would be required to at the first available opportunity elect a President meeting the constitutional requirmenents, if within time period of less than half of a full term (4 years), it will be on the next scheduled election cycle, if more than that, a special interim presidential election would have to be conducted in a joint session of Congress as soon as it can be reconvened, with the representatives and senators serving as electors for an interim period, and the person elected again, must pass the constitutional requirements, and will serve until the next scheduled presidential election.
In plain english.. Had something happened in mid 1999 to Clintoon and Gore and Hastert and Thurmond, Madeline Halfbright would have been president till after the 2000 elections. Before that, it would have been until Congress reconvened, they would act as electors, and that person would fill the unexpired term.
Chao wouldn't be a bad POTUS, remember her hubby is god, err Mitch McConnell.
as for the change in sequence, pursuant to Article I and the 25th Ammendment, I believe this is unconstitutional (when it gets down to departments, line of succession goes by order of cabinet department creation--since War Department was merely renamed Defense Department, it maintained its position.).