Yes, i also surf all the sites at the same time.
But, it becomes tricky when there are more than 5 sites on the Luke page
or one of the site is included twice in the hunt (start and end of the hunt)
Also to note that the order to surf the sites change after a period of time.
For me on the same date (30/07), i had to surf Gauntlet twice.
But the technique you mention, helps to save time.