hadith whose 12er or sunni as to you sunni hadith on leadership are useless and vice versa....according to sunni hadith Prophet predicted 30yr righteous caliphate then kingship and told muslims to follow his righteous caliphs
Quran by itself Quran does not name anyone as successor of Prophet , there might be some indirect hints of method of leadership but without backing them with hadith no person can be judged as successor.so Quran alone cannot be used
"popular stories" what do u mean by that are u discrediting all historians as story tellers ? or only those who dont conform with your views
Hadith
I will reject any hadith, be it Shia or Sunni, that contradicts the Quran regardless of who and where its coming from.
30 years of righteous caliphate = if you guys believed this hadith to be true then your opinion about Ayesha should be different because she rebelled against the righteous calipha (and clearly violated few commands of the Quran in the process).
Quran
The book of Allah does not name successor but very clearly gives qualities and attributes of a leader and a model of leadership. Quran does not name Imam Ali but there are two ways to refer to someone. You can just simply bring his name, or you can refer to his descriptions and attributes. If i asked you to know who your professor for English is then you can either simply bring his name, or you can say, "I have a professor who's very bright, he has the best of morals, he always has a bright smile on his face, he never derides anyone, he's punctual and on time, etc...". The second way is far more effective, especially if you assume that only this professor have this attributes. So the one who wants to know who he us, we will do his research to figure out which professor fits these descriptions. The Qur'an is full with references to Ahlul-Bayt, and the descriptions it gives only apply to them. It does not mention specific names for reasons better known to Allah (swt). If you wish to discuss this topic in details in the light of Quran then i will be very happy to do so.
Popular stories
Well the benchmark for me is not compliance with my view but the person's love and loyality to the Ahlul Bayt (as) of the Prophet (saww). Loving them is the wage of Risalat and if you knowingly deny the wage then you are nothing but a hypocrite therefore untrustworthy and a storymaker.