[texhax] \bigcupdot / \bigdotcup in LaTeX

[Soeren D. Schulze]

I've been wondering how to use the \bigdotcup symbol without the
MnSymbol package.

My current hack is not too beautiful, but it works at least in
\displaystyle:

% Uhhh....
\newcommand{\bigdotcup}{\ensuremath{\mathop{\makebox[-2pt]{\hspace{16pt}{\(\cdot\)}}\bigcup}}}

Problem: it absolutely does not work in \textstyle (the \cdot is
misaligned).
Is there some command to define it separately for \displaystyle and
\textstyle?  Or is there a hopefully better definition for the symbol?