Gin- A Christmas Carol- Dickensian Time Travel?

I Couldn't help feeling while watching this that there was going to be some sort of time-travel paradox twist round the corner. Apart from the Kiyoko characters, the parallels between Gin and both the baby-snatcher's husband and the old man he shares a final drink with, made me consider Gin at different points in his life. While this didn't amount to anything explicitly, due to the heavily referenced Christmas themes I wonder whether Charles Dickens' 'A Christmas Carol' played as an influence on Gin's story? Think about the 'fairy' who visited him in the alleyway as he lay battered and broken.... His acceptance of his reality and his mistakes... His redemption on risking his life for the child and his heart warming to Miyuki and Hana.... Bah Humbug?

Would love to know if anyone thought the same and/or has anything to add to this theory because this movie is brilliant and very moving and I will be watching it again at Christmas time!