How do I minimize the number of "unknown unknowns"?
If you wish to minimize the known unknowns, them you would have to explore more studies published in the area you are researching on. Your advisor, provided he is well versed on the topic, could help you out with this. On the other hand the unknown unknowns can only be discovered by exploring the topic yourself with extensive experimentation and see whether the concept has been published before. To know what is really unknown, you would have to know everything that is known.

Well that would be the holistic view. But coming to the practical view, the known unknowns would only point to the knowledge your thesis committee or reviewers know that you don't but aware of. And, unknown unknowns is more or less the same only that unaware of what they know. 

So it would be better to understand the practical implications of your problem and not to get yourself stressed out too much.

Hope this helps.