Back when the DLC was released, the developer release notes said there was a secret way to open NG+. I never saw the method anywhere else, and I found it by accident, so here it is for anyone interested:

At the title screen, where it says start game, press: up, up, down, down, left, right, left, right.

After inputting the directions for the Konami code, the text box saying NG+ is available should appear.

This is from a newly-reset save I did just to make sure.

Normally, the only way to get to NG+ is after you've already beaten the game, meaning you have a plethora of skills already bought before you even get there that make it easier. The code skips that.

How do you know if the code is for you?

• You like the enhanced difficulty of having no sound indicators and the reworked sight mechanic.
  
• You like the upgrade progression and miss it dearly in NG+.
  
• You needed closure on the secret way to open NG+ that the developer hinted at so long ago.

Whatever your reason, enjoy!