So, the very next day of my MP's office reaching out, status changed to Test Invite! Wow! The nudge seems to have worked!!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.