At this point I think the solution is to have a nearby Raspberry Pi or similar detect the chime with a microphone, then send an old-fashioned email. LOL
edit: Actually, can anyone suggest software to do this with? I already have a Pi-alike in the same room.
I've semi-seriously considered getting one of those flashing process lights that you see on industrial equipment and hooking it up to a pi that monitors the power draw through the outlet and lights up whenever it goes high->low.
Oh you can get a zwave or similar power switch that can monitor power usage that does that for you, no custom rpi required. Then you make an automation that sends a push once power is down after an initial increase minimum.
There are also high power zwave switches that should work with driers too.
Don't know about the audio detection software... you might also think about sampling your home power usage and detecting the characteristic usage pattern of your washing machine..?
edit: Actually, can anyone suggest software to do this with? I already have a Pi-alike in the same room.