Just to put a capstone on this post:
Shudder resolved with the installation of new EBC D182 rotors.
Once I pulled the calipers and the splash shields, I could see that the "highs and lows" that I thought was glazing was actually "lows and highs" due to rusting/pitting in the rotor surface.
Seems that only driving the Mini once a week and my notoriously "light touch" on the brakes, either anticipating the NYC street light changes and coasting, or just allowing the gearing and engine braking to slow me was allowing the surface rust that appears in between weekends to eat more deeply away at the disks. I'm guessing that the hard slam on the brakes back on April 21st broke free some "wafering" and that then presented that rough "step transition" from normal high surface to abnormal low "valley of rust out" and created the banging shudder "out of the blue" even though the rusting had been long at work.
New discs and the Mini is a new car again! Thanks to all who contributed thoughts and suggestions along the way.
A quick word of warning for anyone fitting new rotors and the EBC pads with the pink "BRAKE-IN COATING": Do NOT test out an "emergency braking to stop" scenario after initial installation!!
This stuff is SO aggressive that it was locking up my wheels to the point that it took a serious 1st gear and lots of throttle to get the wheels rolling again. Yep, if I either stopped hard and left my foot down for a moment before lifting or if I pumped the pedal and then released when at a standstill, I was unable to roll the car afterward by hand (and yes, my caliper pistons had/have free travel and yes, we even opened the bleed nipple to ensure it wasn't back pressure in the hoses/pipes - it was not either of those things!)
That pink stuff also left a bunch of itself on the rotor if pressed hard, requiring about a half a block of feathering the brake pedal to scrape it off, thunk, thunk, thunking until it cleared.
It seems that the really aggressive pink coating just "bit into" the black "don't rust while sitting around" factory rotor coating (see pic of the rotor covering) and it just wouldn't let go!
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I'm a few hundred miles into the new pads and rotors now and everything is fine, but I strongly recommend heeding EBC's caution in their installation materials: "...using brakes severely ONLY IN AN EMERGENCY..." for the first 200 miles of use!
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