I want to set the following figure:

I managed to recreate it using forest, but for reasons I do not understand, my command \menge, which I use for sets things that the forest trees are much larger than they are. I guess this has to do with the baseline of the trees. What I get is:

I was able to fix this using adjustbox but this is cumbersome. Here is what I have:
\documentclass{article}
\usepackage{forest}
\usetikzlibrary{tikzmark}
\usepackage{adjustbox}
\newcommand{\menge}[1]{%
\mbox{%
$%
\left\{%
\ignorespaces#1%
\right\}%
$%
%\\[-1.5mm]
}%
}
\begin{document}
\begin{figure}
\menge{
\hspace{1em}
\adjustbox{valign=c}{%
\begin{forest}
[VP
[NP$\downarrow$]
[\subnode{vp1}{VP}]]
\end{forest}}
\hspace{1em}
\adjustbox{valign=c}{%
\begin{forest}
[VP
[NP$\downarrow$]
[\subnode{vp2}{VP}]]
\end{forest}
}
\hspace{1em}
\adjustbox{valign=c}{%
\begin{forest}
[VP
[NP$\downarrow$]
[\subnode{vp3}{VP}]]
\end{forest}
}
\hspace{1em}
\adjustbox{valign=c}{%
\begin{forest}
[VP
[geben]
[\subnode{vp4}{VP}]]
\end{forest}
}
\hspace{1em}
\adjustbox{valign=c}{%
\begin{forest}
[\subnode{vp}{VP}
[$\epsilon$]]
\end{forest}
}
\hspace{1em}
}
\begin{tikzpicture}[overlay,remember picture,out=-90,in=90,dashed]
\draw (vp1) to (vp);
\draw (vp2) to (vp);
\draw (vp3) to (vp);
\draw (vp4) to (vp);
\end{tikzpicture}
\caption{Test caption}
\end{figure}
\end{document}
Apart from seeming redundant, my solution does not get the bounding box for the complete figure right. The dashed lines stick out and interfere with the caption.


\vspaceas in my original proposal. A reply to one of my other questions suggested a way to fix the baseline http://tex.stackexchange.com/questions/206728/aligning-several-forest-trees-in-centered-way I included\forestset{begin draw/.code={\begin{tikzpicture}[baseline=(current bounding box.center)]}}after\menge{and this gets the alignment right not bb. – Stefan Müller Jan 11 '15 at 14:18