I feel more than ever you should have went with the option of the two tickets splitting the remaining period in the term instead of the weird hybrid ticket deal.
Not only VP candidates don't get to serve in that role for half a term because they were tied VP, Kingpoleon who gave up his chance to be VP was not approved for a Cabinet role in the confirmation hearing. He can't even claim a consolation prize. Nice collaborating spirit.
I am not in agreement with the theory that splitting the rest of the term between the two tickets would be unconstitutional.
The hold his office for a term of four months is the general duration of a presidential term. I believe it was the intention when it was written anyway. Not all Presidents hold office for four months. If we had a winner after weeks of court cases, there would not have been four months left in office and there would not have been an extension. If a President resigns, someone new becomes President. The new President will not hold the presidential office for four months.
There are special situations and the tie outcome is planned in the law, with the two tickets splitting equally the term one valid option.