Also, your settings for the system and server classes for the webapp contexts look all wrong, and don't match the defaults in the WebAppContext class for jetty-9.4.15.
Your dump shows:
System Classes:
+> java.
|  |  |  |  |  |  |  +> javax.
|  |  |  |  |  |  |  +> org.apache.commons.logging.
|  |  |  |  |  |  |  +> org.eclipse.jetty.continuation.
|  |  |  |  |  |  |  +> org.eclipse.jetty.http.
|  |  |  |  |  |  |  +> org.eclipse.jetty.jndi.
|  |  |  |  |  |  |  +> org.eclipse.jetty.plus.jaas.
|  |  |  |  |  |  |  +> org.eclipse.jetty.security.
|  |  |  |  |  |  |  +> org.eclipse.jetty.server.
|  |  |  |  |  |  |  +> org.eclipse.jetty.servlet.
|  |  |  |  |  |  |  +> org.eclipse.jetty.servlets.
|  |  |  |  |  |  |  +> org.eclipse.jetty.util.
|  |  |  |  |  |  |  +> org.eclipse.jetty.websocket.
|  |  |  |  |  |  |  +> org.w3c.
|  |  |  |  |  |  |  +> org.xml.
       "java.",                            // Java SE classes (per servlet spec v2.5 / SRV.9.7.2)
        "javax.",                           // Java SE classes (per servlet spec v2.5 / SRV.9.7.2)
        "org.xml.",                         // needed by javax.xml
        "org.w3c.",                         // needed by javax.xml
        "org.eclipse.jetty.jmx.",           // webapp cannot change jmx classes
        "org.eclipse.jetty.util.annotation.",  // webapp cannot change jmx annotations
        "org.eclipse.jetty.continuation.",  // webapp cannot change continuation classes
        "org.eclipse.jetty.jndi.",          // webapp cannot change naming classes
        "org.eclipse.jetty.jaas.",          // webapp cannot change jaas classes
        "org.eclipse.jetty.websocket.",     // webapp cannot change / replace websocket classes
        "org.eclipse.jetty.util.log.",      // webapp should use server log
        "org.eclipse.jetty.servlet.DefaultServlet", // webapp cannot change default servlets
        "org.eclipse.jetty.jsp.JettyJspServlet", //webapp cannot change jetty jsp servlet
        "org.eclipse.jetty.servlets.PushCacheFilter", //must be loaded by container classpath
        "org.eclipse.jetty.servlets.PushSessionCacheFilter" //must be loaded by container classpath
Your Server Classes:
|  |  |  |  |  |  |  +> -org.eclipse.jetty.apache.
|  |  |  |  |  |  |  +> -org.eclipse.jetty.continuation.
|  |  |  |  |  |  |  +> -org.eclipse.jetty.http.
|  |  |  |  |  |  |  +> -org.eclipse.jetty.jndi.
|  |  |  |  |  |  |  +> -org.eclipse.jetty.plus.jass. (note this is misspelt!!)
|  |  |  |  |  |  |  +> -org.eclipse.jetty.security.
|  |  |  |  |  |  |  +> -org.eclipse.jetty.server.
|  |  |  |  |  |  |  +> -org.eclipse.jetty.servlet.
|  |  |  |  |  |  |  +> -org.eclipse.jetty.servlets.
|  |  |  |  |  |  |  +> -org.eclipse.jetty.util.
|  |  |  |  |  |  |  +> -org.eclipse.jetty.websocket.
|  |  |  |  |  |  |  +> org.eclipse.jetty. 
        "-org.eclipse.jetty.server.session.SessionData", //don't hide SessionData for de/serialization purposes
        "-org.eclipse.jetty.jmx.",          // don't hide jmx classes
        "-org.eclipse.jetty.util.annotation.", // don't hide jmx annotation
        "-org.eclipse.jetty.continuation.", // don't hide continuation classes
        "-org.eclipse.jetty.jndi.",         // don't hide naming classes
        "-org.eclipse.jetty.jaas.",         // don't hide jaas classes
        "-org.eclipse.jetty.servlets.",     // don't hide jetty servlets
        "-org.eclipse.jetty.servlet.DefaultServlet", // don't hide default servlet
        "-org.eclipse.jetty.servlet.NoJspServlet", // don't hide noJspServlet servlet
        "-org.eclipse.jetty.jsp.",          //don't hide jsp servlet
        "-org.eclipse.jetty.servlet.listener.", // don't hide useful listeners
        "-org.eclipse.jetty.websocket.",    // don't hide websocket classes from webapps (allow webapp to use ones from system classloader)
        "-org.eclipse.jetty.apache.",       // don't hide jetty apache impls
        "-org.eclipse.jetty.util.log.",     // don't hide server log 
        "-org.eclipse.jetty.alpn.",         // don't hide ALPN
        "org.objectweb.asm.",               // hide asm used by jetty
        "org.eclipse.jdt.",                 // hide jdt used by jetty
        "org.eclipse.jetty."                // hide other jetty classes
There is also something else wrong with the setup for your contexts, as you can see by the logs that for the contexts /service and /, that jetty tries to load the JettyJspServlet, fails and replaces it with the NoJspServlet:
NO JSP Support for /service, did not find org.eclipse.jetty.jsp.JettyJspServlet
NO JSP Support for /, did not find org.eclipse.jetty.jsp.JettyJspServlet
However, for the /zxxxxAdmin context, we don't see the failure to load the JettyJspServlet early in deployment, it only fails to load it when the ServletHandler is being started.  I assume this failure is due to your incorrect system and server classes setup, however this should also fail for the / and /service contexts. The fact that it doesn't means there is something else wrong with your setup.
As for the /zimlet context, this appears to be differently deployed than the rest - I see it is an auto-managed bean of the ContextHandlerCollection, whereas the rest of the contexts are added as managed beans of the ContextHandlerCollection. Please provide more details on how you are deploying the /zimlet context.
Jan