So, after learning about some Ant tasks, here's what I came up with:
<path id="warFilePath">
<fileset dir="./tomcat/webapps/">
<include name="myApp-*.war"/>
</fileset>
</path>
<property name="warFile" refid="warFilePath" />
<basename property="warFilename" file="${warFile}" suffix=".war" />
<mkdir dir="./tomcat/webapps/${warFilename}" />
<unwar dest="./tomcat/webapps/${warFilename}">
<fileset dir="./tomcat/webapps/">
<include name="${warFilename}.war"/>
</fileset>
</unwar>
, . stackoverflow ant -contrib, .