Just as a follow-up, I got this to work by:
1) Packaging jogl.all.jar and gluegen-rt.jar as a separate plugin. Additionally, I have a plugin for the rest of the non-native code jars in the sdk/jars directory.
2) Implementing fragment bundles for the respective native code jars
3) Setting the java property jogamp.gluegen.UseTempJarCache=false
When I tried to do the same thing, but with all the managed code in a single plugin, I ran into issues, but I now suspect I had made some other mistakes, as that should work, theoretically, as well.
What will *not* work is packaging up all of the jars in a single plugin. This actually could be made to work, with a newer version of jogl, utilizing a mechanism that they have implemented to automate the selection/loading of the correct native code, but there is an interface incompatibility with those newer versions of jogl and the version that the ESRI Runtime SDK expects, so no go for now.