I found a copy of the relevant class file here; assuming that this is the same as the one that you are using, the culprit is the following comment:
\parskip 0pt % Extra vertical space between paragraphs.
% Set to 0pt outside sections, to keep section heads
% uniformly spaced. The value of parskip is set
% to leading value _within_ sections.
% 12 Jan 2000 gkmt
Sure enough, looking further down in the document we find that in the definition of the section commands, \parskip gets reset. For example:
\def\@ssect#1#2#3#4#5{%
\@tempskipa #3\relax
\ifdim \@tempskipa>\z@
\begingroup
#4{%
\@hangfrom{\hskip #1}%
\interlinepenalty \@M #5\@@par}%
\endgroup
\else
\def\@svsechd{#4{\hskip #1\relax #5}}%
\fi
\vskip -10.5pt %gkmt, 7 jan 00 -- had been -14pt, now set to parskip
\@xsect{#3}\parskip=10.5pt} % within the starred section, parskip = leading 12 Jan 2000 gkmt
That innocuous \parskip=10.5pt at the end means that every time a \section, \subsection, \subsubsection, or \paragraph command is used then \parskip gets reset to 10.5pt. (The command \@sect has the same ending.)
So to reduce \parskip, you need to reduce it each time that you start a section or otherwise. Depending on your needs, a variety of strategies are possible. The simplest would be to have a copy of the class file in the same directory as the TeX file and simply edit out that extra \parskip=10.5pt (actually, edit out both of them: one from \@ssect and one from \@sect). If you need to leave the class file pristine for some reason, then you can redefine these commands in your preamble. The simplest would be to simply copy out the definitions from the class file with the appropriate modifications to \parskip. If you do this, then the copied definitions need to be sandwiched between \makeatletter ... \makeatother.
If you want to be a bit more fancy, you could have the \section commands remember what \parskip is when they are called, then reset it at the end. This would involve hacking three commands from the class file, since the command \@startsection also messes with \parskip. So it would be something like (not tested!):
\makeatletter
\let\orig@startsection=\@startsection
\let\orig@ssect=\@ssect
\let\orig@sect=\@sect
\newskip\orig@parskip
\orig@parskip\parskip % just for safety's sake!
\def\@startsection{%
\orig@parskip\parskip%
\orig@startsection}
\def\@ssect#1#2#3#4#5{%
\orig@ssect{#1}{#2}{#3}{#4}{#5}%
\parskip\orig@parskip}
\def\@sect#1#2#3#4#5#6[#7]#8{%
\orig@sect{#1}{#2}{#3}{#4}{#5}{#6}[#7]{#8}%
\parskip\orig@parskip}
\makeatother