The problem with betting is that it matters whether it is one case of you making the bet or two cases, and you do not know which it is. This is irrelevant to feeling, so feeling is the way to judge the matter.
I agree that it might be hard to notice the difference when it is so small. This is why the case where you have one wakening vs a million wakening is better. Even in that case, it is obvious that the person will feel uncertain whether the coin landed/​will land heads or tails, so it is obvious that they are halfers.
The problem with betting is that it matters whether it is one case of you making the bet or two cases, and you do not know which it is. This is irrelevant to feeling, so feeling is the way to judge the matter.
I agree that it might be hard to notice the difference when it is so small. This is why the case where you have one wakening vs a million wakening is better. Even in that case, it is obvious that the person will feel uncertain whether the coin landed/​will land heads or tails, so it is obvious that they are halfers.