The difference in lengths of the differential pairs are tremendous, which is quite evident in the screenshot. I just don't see how I am supposed to length-match this. Tips will be appreciated!
I found this: http://suddendocs.samtec.com/catalog_english/usb_a.pdf
You are facing problem with routing because your component doesn't have all pins in-line. The part mentioned above has pins in same line and should get you through.