ProFishent and dougr's methods both work. But if you are still adventurous with the transform, it does work.
I've been using surface transforms for several years without any issues. So I had to test your part to see if there was an issue. I just mocked up your part and there doesn't appear to be anything wrong with surface transform. There are three things to check when making this transform, the number of instances in the transform's pattern, the Patch or Use Quilt feature following the transform, and the transform copy option.
1. When you transform and pattern radially, the number of instances in your pattern is one less than the total number of instances. So your transform's number of instances is 7, not 8. If you use 8, the Patch or Solid > Use Quilt feature will fail.
2. Patch can cut and add material all at the same time. However all the edges of the surface being patched must align to existing geometry. When I tried to copy all the surfaces of the cut and protrusion, they didn't completely align to (touch) the edges of the existing geometry. So I broke it into two features.
The cut was easy as a surface transform and patch. I created the protrusion as an extruded quilt with capped ends so I could quickly and easilly transform the quilt. After I transformed and patterned it I used Solid > Protrusion > Use Quilt to convert the original quilt to solid geometry. Finally I used quilt again to change the transform into a solid and then patterned it.
3. Be sure to make a copy of the original feature when creating the transform or you won't get any dimensions for patterning.