[JimBrimble35]

"How do you overcome it?" - don't.

Lots of other good suggestions on here, but I have some commentary on this problem as well.

I experience the same issue when trying to read with greater concentration. I start out and my brain goes crazy thinking about everything in the known universe. If I stick it out and keep trying to read, in about 10 to 15 minutes I notice that my concentration is restored.

10 - 15 minutes may seem like a hefty price to pay to read with attention, but consider this: the problem described here is very similar to many people's experience with meditation. I believe that this type of mental state is a sort of un-bundling for your brain, and once complete, you can better focus on the task at hand. In my experience, the more reading I do, the less time I spend in this state. By the time I finish a book I can pick it up and immerse myself instantly. Instead of viewing this as "waiting so you can read", try thinking of it as your daily meditation, without really needing to try.

I see this less as an impairment due to your skimming habits, and more of a natural process that many people experience.