What's the best method to make a Hyatt booking?

- there seem to a few cashback sites which offer 1%-3% cashback, though various sites seem to restrictions such as minimum earnings etc.
- do any airline shopping portals award more than 1 mile per $ spent when making a booking on Hyatt.com?

On a related note: Is it possible to redeem gift cards for bookings made under the advance purchase rate? (i.e. would the hotel be able to redeem the gift cards and then refund the charge on the credit card?)

Thanks!