The problem with saxon and xep (mentioned here) was that cocoon loaded up saxon twice (I think). Once from xep/lib and once from cocoon/WEB-INF/lib. I copied the xep/lib/saxon.jar to cocoon/WEB-INF/lib and renamed the original. I no longer get the warning about an XSLT 1.0 stylesheet being processed by an XSLT 2.0 processor. I get 2 new warnings, though:

WARN [TP-Processor3] (Descriptor.java:95) - Giving up unable to read descriptor file from /usr/local/apache-tomcat/webapps/cocoon/WEB-INF/descriptor.xml
WARN [TP-Processor3] (Descriptor.java:114) - Giving up unable to read descriptor.xml file from classloader in package org.exist.http

and

WARN [main] (EXistServlet.java:175) - Looking for a valid Parser...
Checking for Xerces, found version Xerces-J 2.8.0 needed version Xerces-J 2.8.1
Warning: Failed find a valid Parser!
Please add an appropriate Parser to the class-path, e.g. in the 'endorsed' folder of the servlet container or in the 'endorsed' folder of the JRE.
INFO [main] (EXistServlet.java:180) - Looking for a valid Transformer...
Checking for Xalan, found version Xalan Java 2.7.0
OK!

So, we need to find out about the warnings AND determine whether uploading big docs in to eXist still works.