There is separate sin for PvP and for PvE. While PvP sin is calculated in points and can not be absolved by Oswald, PvE sin has no calculation: You are either a sinner or you are not.
Every PvE sin committed will instantly make you a sinner and will require you to pay Oswald. The amount of souls you need to absolve your sins is determined by your level. For each level you need 500 souls, so at level 360 you need to pay 180000 souls.
According to wikidot, actions that result in PvE sin are:
Anything that causes disapproval from an NPC or covenant, that requires Absolution to fix:
- Making an NPC hostile, or killing them
- Angering Gwyndolin by trespassing beyond the Darkmoon Tomb fog gate
- Angering Alvina
- Attacking Crossbreed Priscilla
The only kind of PvE sin that cannot be removed is the kind that is obtained by destroying the illusion of Gwynevere. Although Oswald will allow the player to pay for its absolution, it will refresh and be placed upon the player again automatically.
Regarding Eingyi, I'm not sure if he is counted as an NPC or an egg carrier enemy, as according to his wikidot page, killing him doesn't break the covenant. However, if Oswald charges you again, you will have to pay the full amount again, or more if you leveled up since (although at that high a level the souls shouldn't be too hard to come by).
In any way, the different types of sin also have different penalties. The only penalty for PvE sin is that the angered NPC will attack you, and that you can be invaded in Dark Anor Londo after killing Gwynevere. You will not be added to the Book of the Guilty (like you would for getting PvP sin), so you can't be invaded by Darkmoon blades for having PvE sin.
Since you already killed Eingyi, there is no difference if you absolve or not, except for a clear conscience.