Gradient mesh tool in a donut-type shape

Hello
I am trying to use gradient mesh in a donut-type shape. Basically I want the inner and outer circle of the donut to be black and the inner to fade to gray and back. In other words I want the gradient mest to follow the path. Now I realise that gradient mesh cannot do this. So what I did was cut my shape in four and then try to apply gradient meshes -- still it didn't work. Hopefully the below will explain what I am trying to do and what I end up doing!
Thanks in advance for your help
John

Or … if you find time to do some origami (note that it's just a related topic to entertain a little bit).
1. First, turn on Smart Guides in the View menu, set up some construction guides and draw a rectangle that has the same width as the circular guide, but 50 % of the circular guide's height. Like this:
2. Select the rectangle
3. Object > Create Gradient Mesh: 1 row, 4 columns
4. Direct select the top left mesh point
5. Double click the Scale Tool and choose Uniform Scale = 0 %
6. Now, select the second mesh point from the top left and scale it: Uniform Scale = 0 %
Repeat scaling each single mesh point until all direction lines completely scarper.
7. Direct select the lower 5 mesh points
8. Double click the Scale Tool and choose Uniform Scale = 0 %
9. The next step is to direct select mesh point B and drag it onto the circular guide's anchor point W.
10. Now, direct select mesh point D and drag it onto the circular guide's anchor point O.
11. Direct select mesh point A and drag it to the South Pole. Do the same with mesh point E. This is the result:
12. Take the Convert Anchor Point tool, click on mesh point N and Shift drag to the left until you reach the vertical guide G1.
13. With the Convert Anchor Point tool click on mesh point W and Shift drag to the bottom until you cross horizontal guide G3.
14. With the Convert Anchor Point tool click on mesh point O and Shift drag northwards until you cross horizontal guide G2.
15. Finally do the same at S, but note that there are actually two congruent mesh points, so you'll have to fiddle around a bit in order to drag out the direction lines. However, you should be able to get this:
Now take this mesh object and add it to any Symbol library, so that you can use it as a conical grad maker in future sessions where you just draw a rectangle, fill it with a linear gradient, place the symbol on top of the rectangle and execute the Object > Envelope Distort > Make with Top Object command.

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