Actually I tried it and I didn't have a problem doing it your way with follow-me, so I don't know what is stopping you, without checking the file. I placed the sliver for the follow me, and I had to hide the outside face of the shape to click on the sliver for the operation.
There are many ways to do this. You may have less clean-up if you start your sliver shape lower down at the inside edge of the miter. The finish work at the miter is similar but you aren't left with extra geometry inside of the shape. You could have used follow-me on the whole path (including the upper rounding) and it would be faster.
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