Perhaps you can start neo4j by adding -verbose=class to the startup script?
To see which classes are loaded from where? It should then be listed in /path/to/neo4j/log/console.log
The Neo4j installation should only load files from /path/to/neo4j/lib
and /path/to/neo4j/system/lib
If slf4j is loaded from somewhere else we have to figure out how it gets on the classpath for Neo4j.