The following example defines a macro \MaximizeBaselineskip, which puts the whole text in a horizontal box and measures the width and height to get an upper limit for the \baselineskip:
\documentclass{article}
\newcommand{\MaximizeBaselineskip}[1]{%
\sbox0{#1}%
\baselineskip=\dimexpr\ht0+\dp0\relax
#1%
}
\begin{document}
\noindent
\begin{minipage}[t]{1\columnwidth}%
\MaximizeBaselineskip{%
Just some normal text before the math. Go on a bit of a bit longer so
that this wraps into a couple of lines. I wish I had a funny joke to
tell you but I cant remember any. For example,
$\widehat{\Omega_{YOU}^{\hat{XYZ}}}=\mathit{DYNAMICS}$
is a model that I would
like to examine. OK now lets do some more filler text here to see
another line and check out the spacing. If you read this far you
deserve an award.}%
\end{minipage}
\end{document}

Optimized version
Starting from the \baselineskip, found above, smaller value can be tested. Depending on the previous box depth, the maximum value might not be necessary. The following example implements a binary search to find a smaller value.
\documentclass{article}
\usepackage{environ}
\makeatletter
\newdimen\minmax@baselineskip
\newif\ifminmax@todo@
\NewEnviron{minmaxminipage}{%
\begingroup
\toks@=\expandafter{\@parboxrestore}%
\let\@minmaxminipage@baselineskip\relax
\minmax@baselineskip=\normalbaselineskip
\edef\@parboxrestore{%
\the\toks@
\lineskiplimit=0pt %
\lineskip=10in %
\baselineskip=\minmax@baselineskip\relax
}%
\edef\TESTBODY{%
\noexpand\begin{minmax@test}%
\unexpanded\expandafter{\BODY}%
\noexpand\end{minmax@test}%
}%
\edef\BODY{%
\noexpand\begin{minipage}%
\unexpanded\expandafter{\BODY}%
\noexpand\end{minipage}%
}%
\sbox0{\TESTBODY}%
\minmax@baselineskip=\dimexpr\ht0+\dp0\relax
\typeout{* Max: \the\minmax@baselineskip}%
\edef\minmax@upper{\the\minmax@baselineskip}%
\def\minmax@lower{0pt}%
\sbox0{\BODY}%
\edef\minmax@HT{\the\dimexpr\ht0+\dp0\relax}%
% \typeout{* Tr0: \the\minmax@baselineskip\space -> \minmax@HT}%
\minmax@todo@true
\loop
\ifminmax@todo@
\minmax@baselineskip=.5\dimexpr\minmax@upper+\minmax@lower\relax
\sbox0{\BODY}%
\edef\minmax@new@HT{\the\dimexpr\ht0+\dp0\relax}%
% \typeout{* Try: \the\minmax@baselineskip\space -> \minmax@new@HT}%
\ifdim\minmax@new@HT>\minmax@HT\relax
\edef\minmax@lower{\the\minmax@baselineskip}%
% \typeout{* Low: \minmax@lower}%
\else
\ifdim\minmax@new@HT<\minmax@HT\relax
\edef\minmax@upper{\the\minmax@baselineskip}%
% \typeout{* Upp: \minmax@upper}%
\let\minmax@HT\minmax@new@HT
\else
\minmax@todo@false
\fi
\fi
\ifdim\minmax@upper=\minmax@baselineskip
\minmax@todo@false
\fi
\repeat
\typeout{* Min: \the\minmax@baselineskip}%
\unhcopy0
\endgroup
}
\newenvironment{minmax@test}{}{}
\def\minmax@test#1#{\@gobble}%
\makeatother
\begin{document}
\noindent
\begin{minmaxminipage}[t]{1\columnwidth}%
Just some normal text before the math. Go on a bit of a bit longer so
that this wraps into a couple of lines. I wish I had a funny joke to
tell you but I cant remember any. For example,
$\widehat{\Omega_{YOU}^{\hat{XYZ}}}=\mathit{DYNAMICS}$
is a model that I would
like to examine. OK now lets do some more filler text here to see
another line and check out the spacing. If you read this far you
deserve an award.%
\end{minmaxminipage}
\end{document}
A smaller value for \baselineskip could be found:
* Max: 16.20827pt
* Min: 15.70175pt

\lineskipto be sure and set\lineskiplimitto\maxdimen. – egreg Jul 03 '15 at 16:41\hboxI automatically get the maximum depth and height, thus with the default zero\lineskiplimitalways\baselineskipis set and\lineskipis never used. In the updated answer I have improved this by making\baselineskipas small as possible without setting\lineskip. – Heiko Oberdiek Jul 03 '15 at 16:51