Didn't he want to create a horcrux out of Harry, not to kill him? Of course, he could have implanted himself the false memories he shares in ch. 108:

"So what did happen on October 31st? You... tried to turn the baby Harry Potter into a horcrux, either the new kind or the old kind. You did it deliberately, because you told Lily Potter,"

"Very well, I accept the bargain. Yourself to die, and the child to live. Now drop your wand so that I can murder you."

I would mark the baby as my equal by casting the old horcrux spell in such fashion as to imprint my own spirit onto the baby's blank slate; it would be a purer copy of myself, since there would be no old self to mix with the new.

"The resonance in our magic,"

"When I had shaped the baby's spirit to be like my own..."

But that night... that night, I instinctively tried to control the chaotic fluctuations in my magic, even as I felt myself burning up from inside. That was the wrong decision, and I failed. So my body was destroyed, even as I overwrote the infant Harry Potter's mind; either of us destroying all but a remnant of the other.

Or he might have lain, which means that either he did want to kill Harry, or the purpose of all that October 31st was something completely different.

Or did I misunderstand something?