Your doors are white, are they not?
Having your cabinets stained a darker colour (I am a Canadian Citizen
) sounds like a real trick to me. That has to be some sort of varnish with a pigment mixed in. Sounds tricky but I only have a passing familiarity with wood finishes. My best goes out to the guy doing that in your house. By "woodwork" I mean doors and trim. Personally I wouldn't hesitate to paint up the crown.
In your situation I would paint the frame on one acoustic panel to prove the point. Then paint all the frames on all the acoustic panels and further admire that 'look'. Then look up at that crown and make the decision the paint. I'm trying to gently coax you into an accepted convention.
I'd like to see a pic of the mantle. I saw that your cabinets are like a natural oak. Heaven help the guy who goes at that. I would be worried about a blotchy finish. You might be best served by buying a similar cabinet door and letting him provide you with a test piece.