In response to a question, I only have an old, quick-release 5lb tank that ran out of gas a couple of weeks ago. That's what kicked this whole quest off. But it had been working fine.
Contrary to my initially thinking, I don't think the issue is the regulator. These adapters are supposed to allow folks to swap out their 20 lb tanks for a 1lb if the need arises - without having to change or adjust the regulator. I think the problem has to do with these two adapters.
With those two adapters connected to the 1lb propane canister, shouldn't gas start flowing out? Shouldn't I at least hear or smell something? The screw-on "steak saver" adapter, by itself, doesn't cause the gas to flow. I think this is ok. Indeed, some folks seem to store the canisters with these adapters on them (not recommended by the way). My understanding is that when, with this adapter in place, the canister is connected to the next piece of hardware - the adapter that connects to the regulator - then the gas should start flowing. But this isn't happening. Keeping the regulator out of the picture, I simply can't get gas out of the canister with these two adapters.
I'm going to take the two adapters and the canister to my local hardware store and ask them to take a look at things. Maybe I'm connecting them wrong somehow. Or maybe the canister is defective or something. I'll let everyone know what I find out.