As a ST E+, you should be able to get free EC seat assignments on KL. Unfortunately, as it's been stated in numerous threads, KL does not recognize GM as E+ yet.
I'm traveling from IAH-CPH on KL (I'm a DM, partner is GM). I spent 30 minutes on the phone trying to get assigned E+ seats. We are shown as "requested" on the KL site, but those E+ seats haven't been confirmed.
Based on history, it will take some time for this!