I think I'm done answering this question.
In the short 3 or so years I've been at this, there are few questions I've seen (and tried to answer) than "How do you shave with a Kamisori?"
Last week, someone wrote me a rather long email which, while it involved this question, was really a rather indirect "I shave however I want, so why would anyone tell me I'm wrong?" email.
So yeah, here's my response to that email, and pretty much the last time I plan on answering this question.
I'm sorry I haven't replied, I'm not in any kind of trouble, but I guess it just slipped my mind.
Kamisori are used with one specific side against the face at all times. That side is the unstamped "Omote." The stamped side, which has a much more pronounced concave, is the "ura" and it is to be used away from the face.
The use of Kamisori is a tradition. It is the way it is. I can't answer you as to "why" or whatever, but if you look at the blade profile of a Kamisori, it's pretty obvious that the two sides are different, and thus the use is going to fit that profile. If the use was, as you would like, symmetrical, then the blade would be symmetrical.
This isn't a recommendation or advice, this is the way that they are used, much as when you drive you don't use your right foot on the gas and left on the break. It is what it is. Yes, it's difficult. But it certainly can be learned, if you want to learn it. I have learned it, and I know several other Westerners who have done. And of course, everyone I know in Japan who shaves with one does so.
Now, as to whether or not you can do it another way, well, that's the thing about the word "can." Of course you can shave any way you want. You can use your razors to slice garlic like Paulie in Goodfellas. But in that case, then you are forcing the tool to adapt to your skills, rather than adapting your skills to using the razor the way it is designed to be used. You are ignoring the hundreds of years of tradition and use that produced these razors.
In which case, I have to ask: Why have them and use them at all if not to experience that tradition? Western style folding razors, which are naturally designed to shave the way you seem to want to shave, are cheaper, more widely available, and in many ways easier to use.
I hope this answers your questions.
In short: Kamisori are used with the "flat" (meaning much less concave) Omote side against the face. The Ura, the side with a much more pronounced hollow area, as well as the stamps in most Kamisori, is away from the face. Why? That's just the way it is.* Can you do it any other way? Sure, do what you want, but you're missing a fundamental part of the Kamisori experience.
Oh, and hey, a video!
*"That's just the way it is." is a pretty common trait in traditional cultural artifacts. In Japan, Bonsai, Tea Ceremonies, playing go, all have their idiosyncracies that seem at first glance to be irrational, but then, who are we to judge the rationality of hundreds of years of tradition? Just climb out of your ego and enjoy the ride.