I also have a similar random issue. I'm monitoring the midi input into the Windows laptop and, on occasion, there are many cc controller messages being sent randomly. It's not a constant issue but does have a large impact on the VSTs that i'm using as all of a sudden, the release (for the ADSR envelope) for the sound is jumps to 127 or the attack jumps to 127 meaning pressing a key makes no sound. Tried various midi cables and still experience these 'random' midi cc messages from the MKII.
Still investigating and following your post to see if there is a possible fix for this.
