One advice is do not apply for too many cards at the same time. When you apply for a card and if you are rejected this goes onto your record with the Japanese credit agencies like CIC or JICC for six months before it clears off.

After I got my first Japanese CC (on my first try too!) I was feeling lucky but was rejected for the next 2. I figured I would use my first card as much as possible (always paying in full) building up my record. So I waited 7 months (just wanted to be sure that the previous rejections were cleared) before I applied for the same exact card that I was rejected before on (which was the card I really wanted in the first place), and was approved the next day!

Other tips:
As you know living in Japan with a middle name can be a PIA, as Japanese people have only have a family name and a given name, so most applications and forms only have space to input those items. However some places want your full name as it appears on your residency information, which can be funny at times because I said, "there's no box!" . Usually the solution is to input your middle name combined with your first name *with no space in between. Eg if your name is DOE, JOHN ADAMS it would appear as DOE, JOHNADAMS. I thought this was going to be an issue, but it never was. One of my cards issuer corrected my account by adding the space between while another just left it as is. If you leave your middle name off the application altogether, they might ask you to add it or to redo the application with your full name as it appears on your identification documents.

The application will also generally ask the applicant to input their Romaji name the way they wanted to be printed on the card itself (as the form was designed for Japanese people), that's where I just input my family and given name (without my middle name), again this hasn't been an issue either for me.