@Kilian
We had some debate on this in other threads, where there was a clash between mine and Ww's styles. Looks like you went Ww's route, and it didn't work out.
That style, "honest Abe" can work (outright say you are married), but my belief is you need the charisma, looks, or bigger balls than usual to pull it off. Because women can give you "politically correct" or socially acceptable answers, which is often "no".
My advice is to avoid the being married talk, if possible until you have at least kissed her or had sex the 1st time (preferably). You would tell her you are married, in the bed or hotel room, and after sex. High level of hormones and already had sex, many women won't care at that point.
Preferably, say you are about to be divorced or have an open-marriage, where your wife has a boyfriend too. Use either of these 2 stories, irregardless of your true marital status.
When dating her, go for sex on the day you choose to meet. Have location, restaurant, and nearby hotel already in mind. Don't fumble the opportunity.
If you are not going for sex on that day, cut the date off early, like 1 hour. Definitely less than 2 hours. Make some excuse, but explain you are very interested in you meeting her again. Use the short date to setup things for the longer 2nd date. Even have her agree on day or at least possible days. And make sure that the short non-sex date is very "good energy/good feelings". Don't kiss her, just hugging or hand holding. Leave her wanting more, like an advertisement for the next date. On the 2nd/next day, plan it out for sex to happen.
Another point, is many Japanese women can have zero attachment to you, unless sex happens. Until then, you can just be a friend or like a play toy, or she can be very fake or emotionally neutral towards you. Be careful not to add importance or see a connection, in which she doesn't see or share.