Mike, Interesting that you mention this alternative strategy and using the same windscreen with your alcohol stove.
I had a windscreen that I've used with my Brasslite stove (made according the directions on Brasslite's web page, as I recall). I came up with the same idea to try "hanging" that from the edge of the pot but decided it wasn't worth the trouble: the lid didn't fit so well afterward, getting the screen in place required too much futzing, etc. I also had concerns about the heat radiating to the canister with that setup (although I didn't actually compare it to the heat without the screen). I think I might try this setup again, though.
I also only turned the stove up part-way, so I don't think that was it. And the failure was almost immediate so it didn't seem to allow too much room for lowering the heat.
Maybe the pot has something to do with it. I was using an Evernew 1.3L titanium pot. Maybe a narrower one reflects less heat downward onto the windscreen or something.
BTW, I didn't find I had much need for the windscreen anyway, at least on this one trip so far. The couple times where there was any wind to speak of, I just positioned the stove behind some rocks and that seemed sufficient. Water still boiled quickly enough, with no noticeable loss of efficiency.