Reasons why your yuri ship could get gay married despite Japan not having gay marriage (I'm leaving out stuff that's not set in modern Japan):
- Haruka Tenoh/Michiru Kaioh: Haruka is DMAB and genderfluid, she never got it changed in the family register because she spends enough time as a boy that it wasn't worth the effort
- Sorawo Kamikoshi/Toriko Nishina: they just go to Canada to get married
- Nagisa Misumi/Honoka Yukishiro: Too Iconic
- Akira Kenjou/Yukari Kotozume: mistook Akira for a boy again
- Popuko/Pipimi: nobody wanted to tell them no after what happened last time someone tried to stop them.