Does Ng+++ affect dlc?

I finished the game back when it was released and got all achievements and trophies, so I finished it 3 times on ng+ and ng++ but both these runs were rushed and I wasn’t farming or getting any supplies.

I really want to play the dlc but my only worry is that I’ll have to start a new game and go through it until morg just to get to play it.

What do yall think is the best course of action?