One thing you could do is plot out on a map where all the casinos are in the areas you decide to collect. Then concentrate on using strike-bay only for the strikes from the more isolated casinos and for filling in the ones you missed on your trips. Of course, your trips will be to the areas with greater concentrations of casinos. If you find you have extra time, then you can visit a few of the more distant casinos.
That way the chances would be lower of getting duplicates of the ones you already have.
One drawback is not being able to get all the free slot cards and other collectibles from the casinos you decide to skip.