I sketched the gradients of this image in Photoshop and now I'm working on the actual design in Illustrator with gradients/meshes.

The center image is the sketch. On the lower right you can see the vector I'm working on.

As you can see there are rich blacks in the sketch whereas the blacks are not dark enough in the vector version because blacks are all in K without CMY values.

What should I do to make the blacks work as in the sketch? Should I add CMYs to all blacks manually? Or should I create a black color (with CMY) and use tints of it in the gradients/meshes?

Another concern is that if I add CMYs to the black then it cannot be printed in one-color.

I hope it's clear enough