Indeed, that is the key point! Thank you!
Without using the -jar option but adding the jenkins war to the java -cp option expands the classpath of Jenkins itself and I can now use my third-party libraries. The other important piece in your example code is the name of the main class to call. That was not obvious to me, and I was incorrectly using hudson.Main.
The correct class name is executable.Main
In my case, I use the OS version of Jenkins and the command is something like:
java -Xrs -Xmx256m -cp ".;C:\Windows\Sun\Java\lib\ext\*;D:\DEVTOOLS\Jenkins\jenkins.war" -Dorg.kohsuke.stapler.jelly.CustomJellyContext.escapeByDefault="false" executable.Main