My workflow is quite similar. My inbox is my ToDo list, and I get the jitters when I have more than 20 items in my inbox.

One additional element in your first bullet of your new flow: "If the answer is no, it moves to Asana and is then archived."

Often, the sender of the email is expecting me to take action, and I may not need/want/be able to. If I decide I'm not at that moment, I send them a quick response to tell them so they don't harbor that expectation. And I either tell them I'm not going to do it, or it's on my list but not immediately.