Ok I read the end because I saw the answers.
Personally I've never heard of the "honey moon" thing and think it's bunk.
As far as intergrating or assimilation as you put it, I think it's foolish to even try. There are some gaijins here who act more Japanese than Japanese with a greater knowledge of their history and language and they are still gaijins and everybody I know thinks they are weird to begin with.
I saw an interview with Konishiki once, probably the most loved gaijin in Japan and he said he'll always be a gaijin and everything that means.
But here is the thing, Japan needs to grow and evolve like the rest of the world and gaijins bring a lot of spice and variety to Japan that makes it richer. So just be yourself, there is no need to try to be something you aren't. Unless of course you're in the habit of screaming "Usa Usa Usa" in which case I wouldn't do that.
The job thing. I know people who have come and found a job in a day by working the gaijin network in Roppongi, usually bar jobs and such but they do that as they search for better employment. They do some crazy stuff, many just hand off apartments when they leave to friends. It can be done but you got to have some grit in ya if you know what I mean.
And this whole idea that Japan is such a polite kind place is also bunk.