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PGFPlots "fill between" causes polar axis to disappear

Having a bit of a tough time figuring out what tikz/pgf want from me here. I've tried a few solutions from previous askers, and still can't seem to get anywhere. When I use \addplot fill between [of=A and B];, my polar axis disappears completely and no shading occurs regardless of other settings like color and opacity. Here's an example:

\begin{tikzpicture}
    \begin{polaraxis}[axis on top,
        xticklabels={,0,$\frac\pi6$,$\frac\pi3$,$\frac\pi2$,$\frac{2\pi}3$,$\frac{5\pi}6$,$\pi$,$\frac{7\pi}6$,$\frac{4\pi}3$,$\frac{3\pi}2$,$\frac{5\pi}3$,$\frac{11\pi}6$}
        ]
    \addplot+[name path = A, mark=none,domain=0:720,samples=600, black] 
        {3*sin(3 * x)};
    \addplot+[name path = B, mark=none,domain=0:720,samples=600, black] 
        {3*cos(3 * x)};]
    % \tikzfillbetween[of=A and B]{gray, opacity=0.5}
    % equivalent to (x,{sin(..)cos(..)}), i.e.
    % the expression is the RADIUS
    \addplot fill between [of=A and B];
    \end{polaraxis}
\end{tikzpicture}

Another asker found a solution with \tikzfillbetween[of=A and B]{gray, opacity=0.5}, but it doesn't seem to do the job of filling the intersection of the two paths, at least in the context of a polar axis (fill between works beautifully in a rectangular axis!). It does great at filling in the union, but I'm looking for the intersection.

For reference, here's a fill between example from elsewhere in the same paper.

I totally understand if it's just not possible given the current version of pgf, but it'd be neat to know for sure. Thanks so much!

Answer*

Here is a more primitive, yet working way to fill the intersection of both curves.

\documentclass[tikz,border=3mm]{standalone}
    \usepackage{pgfplots}
    \usepgfplotslibrary{polar}
    %\usepgfplotslibrary{fillbetween}
    \pgfplotsset{compat=1.17}
    \makeatletter
    \tikzset{reuse path/.code={\pgfsyssoftpath@setcurrentpath{#1}}}
    \makeatother
    \begin{document}
    \begin{tikzpicture}
      \begin{polaraxis}[axis on top,
            xticklabels={,0,$\frac\pi6$,$\frac\pi3$,$\frac\pi2$,$\frac{2\pi}3$,$\frac{5\pi}6$,$\pi$,$\frac{7\pi}6$,$\frac{4\pi}3$,$\frac{3\pi}2$,$\frac{5\pi}3$,$\frac{11\pi}6$}
            ]
        \addplot[save path=\pathA, mark=none,domain=0:720,samples=600, black] 
            {3*sin(3 * x)};
        \addplot[save path=\pathB,  mark=none,domain=0:720,samples=600, black] 
            {3*cos(3 * x)};
    	\clip[reuse path=\pathA];
    	\fill[gray,opacity=0.5,reuse path=\pathB];
      \end{polaraxis}
    \end{tikzpicture}
    \end{document}

[![enter image description here][1]][1]

[1]: https://i.sstatic.net/TON7X.png

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