Wow, you sure are loyal to Hyatt. Given your situation, I would just use Priceline or Hotwire to get a room unless you are only a couple of stays away from reaching Diamond status. After driving all day, you'll probably just want to crash at the hotel, get up the next day, and then hit the road so you really won't have much time to enjoy the hotel. It would cost you less than $200+tax for all 3 nights with Priceline/Hotwire and you'd have 8K points for a different trip when you have more time to enjoy the hotel.

I would take the northern route since it is the most direct route.