In Premiere Pro, there is a Black & White filter that simply makes the image Black & White with no drop down menu to control the effect. In Photoshop, the Black & White filter lets you convert how each color will be interpreted to a Black & White image. Is there anything similar to this in Premiere Pro? I've found this particularly helpful in still images and want to try this for video.
What your version of Premiere is doing is a simple de-saturation of the colors.
Photoshop has, finally after having to do this "manually" for years, added a color adjustment to the B/W filter.
So, just do the same: First apply color correction filter(s), and then the B/W filter. After the B/W filter is applied, go into the color adjustment filter(s) and adjust until the final wanted B/W look is achieved.