How can one reconcile the Hadith, "Whoever's last words are 'La ilaha illa Allah' (There is no god but Allah) will enter Paradise," with the Hadith, "Allah accepts the repentance of a servant as long as he does not gurgle [i.e., as long as the soul has not reached the throat before death]?"

There is no contradiction between the two hadiths. The first hadith (definition) gives glad tidings of entering Paradise to whoever's last words are "La ilaha illa Allah" (There is no god but Allah), and uttering it is a cause for Allah's mercy, just as repentance before the death rattle is another cause for mercy. And usually, only those who have repented and are steadfast in following the Sharia (definition) are granted a good ending, whereas one who persists in sin will not have a good ending.