The Audiophile's solution, as you've probably guessed, was a very large sound panel. I can't tell if this has provided a less fatiguing laundry experience, but I have tried clapping like a maniac to test the sound stage, which serves, if nothing else, as a self-gratifying standing ovation.
The right thing to do would be to put The Listening Chair in there and run an A/B test with and without the panel. I'd need several demo loads of laundry to test all frequencies, and some graph paper to sketch the distortion spectrum. Who knows, maybe I'd be so impressed with the stereo image of the washer and dryer that I'd stop calling laundry a chore and start calling it a hobby.
And that, my friends, is audio winning.