I'm 99% sure you're right there!!!
Only thing is, who feels like cleaning the smoker right after a smoke-----I always feel like eating!
Maybe while your smoke is in a cooler, wrapped in foil & towels---That would be a great time to take advantage of your idea.
Note: Be careful how wet your soapy water sponge is, and where the water goes in watt burners, like an MES.
Bear
Exactly Bear! My food is wrapped and recirculating when the cleaning begins. No worries about the element. I never let the water fly. I use a scrub bucket and a scrubby pad. You can put a wet scrubby sponge against the window if you have let it cool at all. I don't do it immediately but it is still quite warm when I clean it. I think waiting defeats the purpose. Hitting it soon gets it before the crud dries out and hardens.