Might also take a look at the harmony triggers FAQ and see if it helps at all. It doesn’t say anything about Alexa but it does tell you how to set up a switch and SmartThings is to control a activity in harmony. So then the only thing left is connecting echo to that switch.
Anyway, I just got a call and I’m going to be off-line for a few days but hopefully other people will be able to continue helping you with this.