So they DIDN'T request fingerprints or any additional info, at least not yet - so that's what is frustrating really! There's nothing to classify my application as non-routine, at least as per their definition.
I only hope that MP's office calling them might at least give my file a nudge.
So, the very next day of my MP's office reaching out, status changed to Test Invite! Wow! The nudge seems to have worked!!