Just to keep it light and fluffy I'm gonna say that San is the reincarnation of Eunjae's dog. I know that is very far fetched, but a girl can dream. If Hwan is San, he would basically be killing himself? I can see where you're coming from for the simalarities between San and Hwan, but my money is on San being the dog or nobody at all.
I originally thought San was his dog too with how much they seem to focus on their similarities however, after reading this last chapter about how if Hwan remembered San he would have never attacked him makes me think that San's is some sort of power being. And perhaps his tattoos are some sort of binding? Maybe that's why he doesn't have his memories? But who knows ┑( ̄Д  ̄)┍
I really thought they were going to go that route that San is somehow Eunjae’s dog, because the similarities kept on being pointed out. I am thinking now that was just to be the catalyst for their romantic relationship to start (no matter how weird I find it lol).
The San is Hwan thing is completely crazy I know and most likely not true. But there must be something in SAN’s past that at least connects them I think I just have absolutely no idea what.
I actually really love this theory thank you for the reply!
Maybe he is one of the king of the underworld like Yama or something.
I like the thought that the markings are binding his power, but I thought it was established that the markings come from someone marking you. Since 704 got marked from Eum on the back of his neck from Eum biting him during sex. I might have misread that though and I hope I did cause I look your theory better ヾ(☆▽☆)

Idk if I am losing it or thinking too much into it, but did the guy that essentially raped Eunjae (in the chapter about him losing his family) look like San a little?
I think San was either that guy, Eunjae’s dog or Hwan when he was alive (I can’t explain how this would be possible but even from ch1 I have seen resemblance). So excited to find out and the angst that I am sure will come with San getting his memories back.