So, before I begin, I must inform you all that I do read EPIC, mainly cause of its many neat ideas, though I think the harem has gone a bit off the rails, I can't even remember how many women Vahn has at this point. I pointed this out just to give you a sense of what kind of deviation is possible in Danmachi's world. Of course, since the original story isn't yet finished, there is so much left to the individual interpretation of every reader. And, I should probably make it clear that I don't want god-killing to be the central focus, it will just be the MC's Innate Skill.
Well, I've already given away what the unique draw is just from the title and my last paragraph, but I'll go a little in-depth. So, the MC's Innate Skill will be God-Slayer, which allows him to permanently kill divine beings, as well as absorb their power into himself. It isn't limited to the various gods and goddesses of different mythologies introduced, it can also be used on things of a magical or spiritual nature. It also makes any weapon wielded by the MC capable of piercing divine protections. Any divine energy used on the MC will be rendered inert, making him incapable of receiving a Falna. He will emit an aura that both suppresses and causes gods and goddesses to fear him, even if he means no harm. Spirits and beings of that nature will feel unnerved by him, but this can eventually be overcome. He will still be able to gain strength by defeating monsters but will be unable to see his status. I think that this Innate will eventually grow to become the most overpowered ability to grant a character in Danmachi.
The absorption aspect of his powers should only come into play when there is a God or Goddess that is a real threat, the MC should not be going around murdering whatever divine beings he can find. If you make him this way, it would take away possible character development from him, and it wouldn't make for a very long story. Now let's move on to the character's origins.
So, for this story, I actually don't think that reincarnation or transmigration are the ways to go. This time, I think that an insert would flourish. Think of it, a character with a mysterious backstory suddenly forcing his way into the original plot, shoving Bell out of his spotlight. I feel it's a great idea, and has a lot of potential.