<p>Working in Eclipse on a Dynamic Web Project (using Tomcat (v5.5) as the app server), is there some way I can configure things so Tomcat will start with security turned on (i.e. as if I ran catalina.sh start -security)?</p>

I'm assuming that you're using Tomcat 5.5.x
after looking at catalina.bat/catalina.sh, all the -security flag does is to set 
-Djava.security.policy=="%CATALINA_BASE%\conf\catalina.policy"
Most people have CATALINA_BASE set to TOMCAT_HOME or CATALINA_HOME
So, if you have installed tomcat in the directoryc:\tomcat, then all you need to do is to set an option in the tomcat plugin to include the above policy.
i.e, add this to JAVA_OPTIONS : -Djava.security.policy=="c:\tomcat\conf\catalina.policy".
That's all and restart.