I have a profile that I want to be swept following a path, up to a face.

The problem is that the face is not planar, i.e. it's a cylinder.

I can mate the path endpoint to the cylinder. However, the sweep is not gonna extend up to the cylinder face, it stops right at the profile endpoint. There is no option in the sweep feature to have the sweep continue "up to next" or "up to surface", like in the Extrude feature.

Sure, I can make the path longer then use surface cut, or I can shorten the path and add an extrude feature at the end of it to extend to the cylinder, but those are not elegant solutions.

What's the most elegant way to do this?