Safar 10, 1330
Those who follow the Sunnah and consensus deny this will simply because of what alBukhari has narrated in his Sahih where he quotes alAswad saying, "It was said once to ‘Ayesha, may Allah be pleased with her, that the Prophet (pbuh) had made a will regarding ‘Ali,1 and she responded: ‘Who said so? I have seen the Prophet, while I was reclining him to my chest, when he ordered a washbowl to be brought to him; I hardly noticed how fast he collapsed and died; so, how could he have made a will to ‘Ali?"2
In the same reference, the author quotes other sources citing ‘Ayesha saying, "The Messenger of Allah breathed his last while being between my stomach and under my chin," and she is often quoted saying, "He died reclining on my chest," and she may have said: "He died while his head was on my thigh."3 So, had there been any will, she would have come to know about it. In Muslim's Sahih, in a treatise on the subject of wills on page 14, Vol. 2, the author quotes ‘Ayesha saying, "The Messenger of Allah (pbuh) left neither a dinar nor a dirham, nor a male nor a female camel, nor did he leave any will."
In both sahihs, in a treatise on wills, Talhah ibn Masrif is quoted saying, "I asked ‘Abdullah ibn Abu ‘Awfah: ‘Did the Prophet leave any will at all?' He answered: ‘No.' I asked him: ‘How did he enjoin people to write their wills while he himself did not do so?' He answered: ‘His will is the Book of Allah.'" Since these ahadith are more authentic than the ones which you have cited, and are included in both sahihs, while the ones you have cited are not, they can be brought forth as irrefutable arguments, Wassalam.