I'm less of a practicing Muslim now, but I've always held that being a Quraysh wasn't a literal group of people with a shared common patrilineal descent. Bani Shaiba being R1a has proven that in my mind and I would like to know more about how their R1a ended up in the Hejaz to begin with.
In addition, Bani Tamim is a humongous Arab tribe and have many clades that are outside of J1. I don't think Arab culture pre-Islam was necessarily opposed to absorbing another family, adoptions, letting freed slaves join, etc. which would make a larger tribal confederation more heterogeneous.
The Shia point-of-view of history has asserted that Umayya (progenitor of the Ummayads) was adopted by Abd Shams and was a "Roman slave boy". If this view is correct then this could mean that he's E, J2, G, or something even more exotic for the Middle East like R1b or I and that there is no consistent Quraysh haplogroup because of further diversity.
When it comes to Bani Hashim there should only be one 'right' Y-DNA'. I still believe that the J-FGC10500+ clades downstream of L859 are the best candidate but I'm admitting that I'm only agreeing with the consensus on FamilyTreeDNA, the convenient age of the mutation, and the fact that there are a large number of claimants to being a Sharif/Syed on that line. I'm willing to update my beliefs if proven wrong.