Would I also have to itemize and overcome the standard deduction for it to be beneficial?
Not necessarily. It would probably help regardless but again we need numbers.
Keep in mind that even if the standard deduction is better this year, that might not be so a few years from now. Also, you may have substantial 401(k) or IRA contributions that you are also deducting ten years from now.
That said, unless you have a lot of student debt it may not be worth the expense of refinancing. And if you do have a lot, you may not be able to borrow enough. Again, numbers are needed.