I know it was the intention, but it doesn't actually work the way you think.
The thing that causes the confusion is that you introduced an infallible decision maker into the brain that takes all autonomy away from the human (in case of there being no forecaster). This is basically a logical impossibility, which is why I just said "this is newcomb's problem". There has to be a forecaster. But okay, suppose not. I'll show you why this does make a difference.
In Newcomb's problem, you do in fact influence the contents of the opaque box. Your decision doesn't, but the fact that you are the kind of person who makes this decision does. Your algorithm does. In the Alien Implant scenario case no forecaster, you don't affect the state of your box at all.
If there was a forecaster, you could prevent people from dying of cancer by telling them about Timeless Decision Theory. Their choice not to smoke wouldn't affect the state of their box, but the fact that you convince them would: the forecaster predicts that you prevent them from smoking, therefore they do not smoke, therefore it predicts they don't smoke, therefore the box is on state 2.
If there was no forecaster, whether or not you smoke has no effect on your box, causally or otherwise. The state of their box is already determined; if you convinced them not to smoke, they would still get cancer and die and the box would be on state 1. Now this never happens in your scenario, which like I said is pretty close to being impossible, hence the confusion.
But it doesn't matter! Not smoking means you live, smoking means you die!
No, it doesn't. Suppose the decision maker was infallible. Everyone who smokes dies. Sooner or later people would all stop smoking. And this is where the scenario doesn't work anymore. Because the number of people dying can't go down. So either it must be impossible to convince people – in that case, why try? – or the decision maker becomes fallible, in which case your whole argument breaks apart. You don't smoke and still die.
Think about this fact again: no forecaster means there is a fixed percentage of the population who has their box on state 1. If you are still not convinced, consider that "winning" by not smoking would then have to mean that someone else gets cancer instead, since you cannot change the number of people. Obviously, this is not what happens.
If there was a forecaster and everyone stopped smoking, no-one would die. If everyone one-boxes in Newcomb's problem, everyone gets rich.
I'm not sure what you mean by "autonomy" here. The scientists guess that the device is reading or writing, but a third possibility is that it is doing both, and is a kind of brain computer interface. In essence you might as well say it is part of the thing there: the human-black box combination has just as much autonomy as normal humans have.
"Suppose the decision maker was infallible. Everyone who smokes dies. Sooner or later people would all stop smoking. And this is where the scenario doesn't work anymore. Because the number of people dyin...