Amazon is actually terrible with Emergency Shutdown, as you're paying to rez ICE before they even stop the runner once, and it doesn't provide a recurring benefit like Akitaro. If you're looking to screw over Emergency Shutdown, you should grab him instead. This deck will also get run over by Anarchs as their efficient breakers will run rampant here until you can Chum something, in which case they'll use Parasite/Datasucker to easily get past it.
Ultimately I think Weyland is still devoted to big ICE like Archer, and needs to beat Emergency Shutdown with good play rather than trying to do something that Jinteki, NBN, and even HB does better than them.
I mostly agree with you about wanting some big Ice in Weyland, but I did want to point out that a quick check of the Ice in this deck reveals that none of it costs more than 3. So you actually don't pay to rez Ice when you're using Amazon. Which is actually a pretty interesting approach.