Vertically center when using overlayarea

Question

Consider the following MWE:

\begin{frame}
  \frametitle{Foo}
    \begin{overlayarea}{\textwidth}{0.8\textheight}
      \begin{center}
        \input{big_tikz_image_with_many_overlays.tex}
      \end{center}
    \end{overlayarea}

    \begin{overlayarea}{\textwidth}{0.15\textheight}
      \begin{center}
        \only<8->{%
           Some text
        }
      \end{center}
    \end{overlayarea}
\end{frame}

Here, the TikZ element in the upper part has several overlays, and the "Some text" should appear from slide n and on. In order to avoid "jumpy" slide I used the overlayarea environment. The problem is that when using this environment, the vertical centering of the content is broken. The two blocks are pushed towards the upper part of the frame. I tried to add \vfill between the two, but it didn't help.

How can I vertically center the content of the frame? Maybe, somehow enclose the two areas in a bigger box?