Making a patterned cut around a cone-like shape

[Weekdayweekend]

How should I go about making this cut properly?
It's a cable winder, and the cutouts are there to tuck the ends of the cable in. But Because of the cone-like shape, I can't sketch directly on the surface I want to cut into. I tried a wrap, but since it wants to wrap over the edge, it doesn't quite work and it just errors out.
If it isn't clear, I basically want to do an extrude cut that's along the same angle as the cone-like shape. Anyone know a good video? I'm not sure what to even call this kind of an operation, so I don't even know how to look it up.
Ignore the dimension it's showing, it's an artifact of the current method I've tried for the cut, which is just to sketch the shape, do a midline extrude cut, and circular pattern that...

 

[Stu3d]

Have you tried a new plane offset from your part, draw the cutout on that and then extrude cut through the part?
Edit, in fact you could just draw the cutout on one of the 2 planes your part is not drawn on.

 

[Weekdayweekend]

I have, and it works the same. My main issue is that it doesn't follow the curvature of the part. That is, the inside has a larger cut than the outside, or vise-versa, because of the shape.

 

[Stu3d]

Does a plane at the same angle as the cone face help?

 

[Weekdayweekend]

That would probably do it! I was way over-complicating this, I think. In that photo, did you just make a new plane by rotating the XY plane?
EDIT: Yup, got it. I think that will fix all my problems. I was really overthinking it. Thank you!

 

[Stu3d]

Yes