I'm with Eliza - I thought you'd already concluded that ink blue was your black! It's an excellent choice for you. I'm impressed that you have found so many important pieces in it, too; it's difficult to find for me.
I don't have a new black, but nor do I have an old black. I don't actually wear a whole lot of neutrals, period. That's part of why Duchess Kate is such a good icon for me - she focuses on color in dresses and coats, with the neutrals only showing up for shoes, hats, and clutches. When I wear separates I rely on white or black skirts and shoes (and legwear in the cold), depending on the season and primary color(s) I'm setting off. Rose gold is my nude footwear.
So I couldn't do without black, and it would be tricky to simply replace black with ink blue - I'm so picky about color combinations, it just won't set off royal blue and red and various greens in the same way as black. But black isn't "the black" for me, because I don't love it. I own no black tops, and my only black dresses are choir uniform. Black only exists to complete outfits.