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,$fracpi6$,$fracpi3$,$fracpi2$,$frac{2pi}3$,$frac{5pi}6$,$pi$,$frac{7pi}6$,$frac{4pi}3$,$frac{3pi}2$,$frac{5pi}3$,$frac{11pi}6$}
        ]
    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!

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,$fracpi6$,$fracpi3$,$fracpi2$,$frac{2pi}3$,$frac{5pi}6$,$pi$,$frac{7pi}6$,$frac{4pi}3$,$frac{3pi}2$,$frac{5pi}3$,$frac{11pi}6$}
        ]
    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}