That's confusing!
"...one of whom..." Does that mean "exactly (or "at least?") one member of the set consisting solely of the P. and V.P. not being an inhabitant of the same state as the other member of that set?"
That could have been expressed much more elegantly: "...and vote by ballot for P. and V.P.; the P. shall not be an inhabitant of the same state as the V.P."
Regards,
Your rewrite prohibits the President and Vice-President from being from the same state.
The Constitution does not prohibit this, but if they are from the same state, that state's electors must choose between them and likely cast their VP vote for someone else.
This almost became an issue with Dick Cheney, who was residing in Texas in 1999 as CEO of Halliburton. Cheney had to change his residency to Wyoming (the state he represented as a Congressman) in order to qualify for 12th amendment Electoral votes. As we now know, those votes mattered, since President Bush won with 271 Electoral Votes.
If Bush/Cheney had decided to take a chance and have Cheney remain a Texas resident, Cheney would not have received a majority of appointed Electors and the Senate would have chosen between him and Joe Lieberman in the first week of January 2001. The 2000 Senate election resulted in a tie 50-50, so Al Gore as Vice-President would have broken the tie with a vote for Lieberman.
-PJ