I have a star in which I've used the rounded stroke join style with a wide stroke, to make the points nicely rounded. I want to put a semi-transparent gradient on top of it, clipped to the outer edge of the stroke. Here's a sample image:

On the left is the base star image. Center is the base image (which can't be seen at this point), plus a gradient (that I just threw together for this illustration), with the dark blue star, which is the actual clipping path, on top. On the right is the result of the clip. But I've lost my nicely rounded tips

I also tried Difference, but got the same result as clipping.
I know what's happening. It's using the path of the star, to do the clip and difference, rather than the stroke. My question, how to clip away the gradient and end up with the star PLUS the wider stroke, like the blue stars are shaped?
I also tried applying the same gradient to both fill and stroke. But again, the wider stroke trips me up. Here's an illustration:

Because the gradient is partially transparent, the area of the stroke that falls inside the path sort of doubles the gradient over the fill area, creating sort of a framed effect.
I've tried to get the shape of star I want, using the Star tool, but I can't seem to get it right.
What I want is for the finished product, the gradient, to be shaped like the 2 light blue stars on the left, and like the dark blue star that I tried to use as the clipping path in the 1st example -- fill + stroke. How can I achieve that?
I'm thinking I could use Stroke to Path, to make the clipping path, but that alone won't do it. Then I'll have to fool around with nodes and stuff to get a solid fill. Is this the only way to do it? Otherwise, how can I achieve a clipping path that's shaped like the star WITH the wider, rounded stroke?
I know you wise and wonderful Inkscape folks will know some clever way to do exactly what I want

