You made the icedtea6 package also?
For Java GUI support, the Jalimo project has packages for the SWT. For deployment, you could use debian packages. the Jalimo page describes a maven plugin to make deb packages. The Jalimo SWT looks native and works well for me.

If you include the files from the SWT JNI package in jre/lib/arm and the jars from the SWT package in jre/lib/ext (both can be found here), SWT-based GUI apps work with java -jar. This Java developers can put into .desktop files in debian packages.
I have made this Java app that assumes java is in the path and swt installed. It works after the install of the Jalimo SWT example from here (Single Click Install link).

I have also tested it with an optified openjdk from debian sid, and your icedtea6. Both seem to be good as long as the Jalimo SWT is installed. The Jalimo virtual machine however uses GNU Classpath, and is not fully compatible with Sun's class library; for example HTTP connections do not support chunking.

So in my view, the best possible Java we can have is icedtea6 + SWT from the Jalimo project. For the Java web plugin, I don't know how to proceed.

P.S. I also tried microEmulator, but it seems my MIDlet never creates any other commands than Quit in it, and keys also seem to do nothing. It's like the microEmulator virtual phone is active, but the MIDlet UI inside it is frozen.