If Sweet Home 3D works in 2D, I'm not even sure you'll have to recompile anything and you shouldn't have to care about JNLP.
You should replace Java Runtime like you did and the DLLs [font=courier new]libjogl_desktop.so[/font], [font=courier new]libnativewindow_awt.so[/font], [font=courier new]libnativewindow_x11.so[/font] and [font=courier new]libgluegen-rt.so[/font] used by Java 3D, by the ones for ARM found in jogl-all-natives-linux-armv6.jar and gluegen-rt-natives-linux-armv6.jar.