RVDB sent a solution to my Ant build problem, which basically works -- the eXist build.sh is now found -- so I've integrated that, and I've also found a better solution to using Saxon for XSLT, that doesn't depend on its being on the CLASSPATH (which I want to avoid, because its version numbers are likely to change over time). I found the solution in one of the comments on this page, and it's basically this:

1. Define a macro for Saxon, specifying a way to call it with the parameters we need to use:

     <macrodef name="xslt-saxon">
       <attribute name="in"/>
       <attribute name="out"/>
       <attribute name="style"/>
       <sequential>
         <echo level="info">XSLT Generating @{out}</echo>
         <java classname="net.sf.saxon.Transform"
           classpath="${saxon.home}/saxon9he.jar"
           logError="true"
           output="@{out}"
           fork="true">
           <arg value="@{in}"/>
           <arg value="@{style}"/>
         </java>
       </sequential>
     </macrodef>
   

2. Call the macros when required like this:

   <xslt-saxon in="${cocoon.home}/build/webapp/WEB-INF/cocoon.xconf" 
               style="cocoon/patch_cocoon_xconf.xsl" 
               out="${cocoon.home}/build/webapp/WEB-INF/cocoon.xconf.patched">
   </xslt-saxon>
   

Now I have RVDB's whole build process working OK, but the resulting webapp is broken; XSLT transformations don't seem to work. I suspect this is something to do with the way Saxon is being set up in the sitemap, because I'm using a more recent version of Saxon (HE, 9.3, as opposed to the three-jar version 9). I'll work on this issue tomorrow.