I don't think i've ever seen a motherboard with 6 sata3 ports, even the most expensive, top of the range mobo's; The most i've seen is 4 in the Asus Maximus extreme-z.
My advice would be to either lower how many sata3 ports you need or significantly raise your budget.
TBH I don't think there's a huge amount of real-world difference between sata2 and sata3 anyway.