It's not surprising that what you call a tumbler (Really a dry tumbler, the proper term is vibrator.) or a lemishine bath wouldn't touch serious tarnish. It's just not going to work for you.
IDK how well ultrasonic cleaning works, but there are other likely cheaper options.
Sorry to be an advocate for "unobtainium pins in a Mr Fusion cryogenic centrifuge," but a real wet tumbler with SS pins is the most cost effective way to really clean the brass.