In the extrude toolbar, under extent, there's an option for Through Next which will do what you're asking. Or alternativly you can do from/to extent to go between two curved surfaces.
Maybe this explains a little better. I want to use the sketch to cut co the cylinder face, through the support and rounded edges.
I think your stuck with this one, or a long work around. Project and include ONLY work normal to the target, not normal from the source. The only way to get this done at all is to figure out the sale factor going around the bend, and do a scale to the coordinates of the desitation along one axis and map out the point.
I hope I'm wrong but that's my current understanding.
I'm an ordered sheet metal guy. Look at the blue surface stuff, it looks like there are some tools there that could help. I noticed that today while trying to do some weld creation.
If there are any class A surfacing guys around, they will have the good info. I did that stuff in Imageware, but not in SE yet.
Are you trying to cut up to the inside curved face of the radial slots? If so, you can make your cut with the circle using the finite extent option but leave it short. Then use "replace face" in surfacing to pick the inside wall - you will probably also need to pick the fillets as well. Doing so will also consume the fillets. If doing this in ordered, I recommend doing the cut operate before the fillets.
I just realized there is a better way to employ replace face. Go ahead and let the cut penetrate the inside wall of the radial slot. Then use replace face to fill in the excess depth. That will preserve your fillets so you don't have to re-order them.