I would use a slightly lower level PGF (Portable Graphics Format) command \pgfpatharcto
for this and I have guessed the 11cm by eyeballing. For the bonus I created a scope where I defined the x unit vector to be (-1,0)
so whatever is drawn inside, the horizontal coordinate will be reversed. Hence, I can literally copy the right part code into left part except the arc command which accepts absolute coordinates (unless there is any coordinate transformation is going on).
\documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\filldraw[fill opacity=0.5,fill=yellow] (0,0) ellipse (7.0 and 4.3);
\draw[line width=5mm] (0,0) ellipse (6.5 and 3.8);
\draw[line width=2pt,dashed,white] (0,0) ellipse (6.0 and 3.3);
\draw[line width=2pt] (0,2.7) -- (0.5,2.7) -- (1,3.25)
.. controls (1.2,1.3) and (1.3,1.0) ..
(2.0,1.0) .. controls (3.0,1.0) and (3.0,2.2) .. (2,3.1);
\draw[line width=2pt]
(3.2,-2.8) .. controls (4,-2) and (4,0) .. (2.2,-1.8)
.. controls (1.5,-1) and (1,-1) ..(0,-3.2);
\pgfsetlinewidth{2pt}
\pgfmoveto{\pgfpoint{2cm}{3.1cm}}
\pgfpatharcto{6cm}{3.3cm}{0}{0}{0}{\pgfpoint{3.2cm}{-2.8cm}}\pgfusepath{stroke};
\begin{scope}[x=-1cm]
\draw[line width=2pt] (0,2.7) -- (0.5,2.7) -- (1,3.25)
.. controls (1.2,1.3) and (1.3,1.0) ..
(2.0,1.0) .. controls (3.0,1.0) and (3.0,2.2) .. (2,3.1);
\draw[line width=2pt]
(3.2,-2.8) .. controls (4,-2) and (4,0) .. (2.2,-1.8)
.. controls (1.5,-1) and (1,-1) ..(0,-3.2);
\end{scope}
\pgfsetlinewidth{2pt}
\pgfmoveto{\pgfpoint{-2cm}{3.1cm}}
\pgfpatharcto{6cm}{3.3cm}{0}{0}{1}{\pgfpoint{-3.2cm}{-2.8cm}}\pgfusepath{stroke};
\end{tikzpicture}
\end{document}

EDIT2 : Filling the curve was much difficult with the code above so making a continuous path seemed easier since Damien already provided the necessary coordinates. There is simply no complication other than renaming the commands. The \pgfpathcurveto
is equivalent to \draw (coord1) ..controls (support1) and (support2) .. (coord2)
except that you have to move to (coord1)
first. After the coordinate transformation, it is again a matter of copy-paste.
\documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\filldraw[fill opacity=0.5,fill=yellow] (0,0) ellipse (7.0 and 4.3);
\draw[line width=5mm] (0,0) ellipse (6.5 and 3.8);
\draw[line width=2pt,dashed,white] (0,0) ellipse (6.0 and 3.3);
\pgfsetlinewidth{2pt}
\pgfpathmoveto{\pgfpoint{0}{2.7cm}}
\pgfpathlineto{\pgfpoint{0.5cm}{2.7cm}}
\pgfpathlineto{\pgfpoint{1cm}{3.25cm}}
\pgfpathcurveto{\pgfpoint{1.2cm}{1.3cm}}{\pgfpoint{1.3cm}{1cm}}{\pgfpoint{2cm}{1cm}}
\pgfpathcurveto{\pgfpoint{3cm}{1cm}}{\pgfpoint{3cm}{2.2cm}}{\pgfpoint{2cm}{3.1cm}}
\pgfpatharcto{6cm}{3.3cm}{0}{0}{0}{\pgfpoint{3.2cm}{-2.8cm}}
\pgfpathcurveto{\pgfpoint{4cm}{-2cm}}{\pgfpoint{4cm}{0}}{\pgfpoint{2.2cm}{-1.8cm}}
\pgfpathcurveto{\pgfpoint{1.5cm}{-1cm}}{\pgfpoint{1cm}{-1cm}}{\pgfpoint{0cm}{-3.2cm}}
\pgftransformcm{-1}{0}{0}{1}{\pgfpointorigin} % This is the coordinate change from x to -x
\pgfpathcurveto{\pgfpoint{1cm}{-1cm}}{\pgfpoint{1.5cm}{-1cm}}{\pgfpoint{2.2cm}{-1.8cm}}
\pgfpathcurveto{\pgfpoint{4cm}{0cm}}{\pgfpoint{4cm}{-2cm}}{\pgfpoint{3.2cm}{-2.8cm}}
\pgfpatharcto{6cm}{3.3cm}{0}{0}{1}{\pgfpoint{2cm}{3.1cm}}
\pgfpathcurveto{\pgfpoint{3cm}{2.2cm}}{\pgfpoint{3cm}{1cm}}{\pgfpoint{2cm}{1cm}}
\pgfpathcurveto{\pgfpoint{1.3cm}{1cm}}{\pgfpoint{1.2cm}{1.3cm}}{\pgfpoint{1cm}{3.25cm}}
\pgfpathlineto{\pgfpoint{0.5cm}{2.7cm}}
\pgfpathclose
\pgfusepath{fill,stroke}
\end{tikzpicture}
\end{document}
EDIT3 Alfred, join this curve nicely will ya? So we draw one half and carry on backwards for a proper line join at the tail and fill.
