Thanks @vitor, this workflow is truly a game-changer and I've already been using it quite a bit.
One issue I found: if you open the Alfred prompt, start querying ChatGPT with the set keyword (I changed mine to "c"), and then hit CMD-Enter (which should start a new chat session), the Alfred prompt disappears and doesn't show any results. If I had invoked it normally (with just "Enter") it works fine, but with "Cmd-Enter" it does not.