I know that there were various laws passed over almost two centuries (1792, 1886, and 1947) trying to rectify the problem, but was there no recognition from lawmakers at the time that there remained glaring uncertainties?
Even Article II, Section 1 of the Constitution is murky at best. Did the Founding Fathers not realize this? Or were they simply kicking the can down the road?
What the founding fathers intended with Art. II section 1 was the determine that the Vice President assumes the roles and responsibilities of the president until a new president is instated. That doesn't necessarily mean that he IS president. It means that he has his job, temporarily, until things can get sorted out politically after a disaster.
I would personally speculate that the reason for this is because it's very likely that a Vice President might not be willing or able to take on the full presidency in the event of the death of the president.
Not to mention the possibility that the founders were concerned the Vice President would execute an assassination to attain power.