But as originally presented in the op, there's only one coin toss. After that, the experiment ends. So I still stand by my 1/2 position answer.

Edit: I re-read the first post, just to make sure, and it says that Sleeping Beauty is made aware of all details of the experiment before it starts. Therefore, she would certainly have all the more reason to take the 1/2 position.

Disallowing environmental evidence that might help her decide the actual date, there's no reason for her to think that the coin toss was anything other than 50/50. If there's only one trial, this is the right answer.
For a thousand trials, though, heads will be wrong 2/3 of the time, because there will be twice as many tails interviews as heads interviews. However, this only applies if each interview is cataloged separately. If the interviews are cataloged on a per-flip basis rather than a per-interview basis, it goes back to 1/2 because being wrong twice doesn't matter any more than being wrong once. So how the "correctness" of her guess is being recorded makes a huge difference on the results.

As mentioned before, it seems like the only issue is the proper definition of the question. If you talk about one interview, this looks like a simple two-stage experiment: a fair toin coss, giving 50% to heads and tails, then in the tails case another 50%-50% split between the two days, as they are indistinguishable for her. If, on the other hand, you ask for the expected number of right answers during the course of a whole test run, tails wins (2 right answers in 50% of the cases vs 1 right answer in 50% of the cases).

Heads = 1
Tails = 2

However, this implies that the scientists don't lie. Scientists generally have to be assholes, so from psychological experience the probability that the coin landed on this or that side simply doesn't matter at all.

Since in 50p of the cases you get 1 and in 50p of the cases you get 2, otherwise the probability would be:

1 vs. 2 for the awakening events
1 vs. 1 for the coin probability

Since at one of the results one right and one wrong outcome are achieved, and at the other result two right outcomes are achieved, the probability is actuall 1/4 for heads and 2/4 for tail. The other possible 1/4 for heads simply doesn't apply because she would be asleep there. And this is what was not looked at in the paradoxon!

The probability is:
Heads = 0.25
Tails = 0.5

Surely at a casual examination this would look like 1/3 vs. 2/3 but with a probability of 1/4 she is NOT INTERVIEWED! Namely on Tuesday after Heads. This also influences the probability. So we have three events.

Interview on Heads: 1/4
No Interview on Heads: 1/4
Interview on Tails: 2/4

So the correct answer is neither 1/2 nor 1/3 but rather 1/4. If the interview takes place then one of the four possibilities just does not occur. Therefor she has a probability of 1/4 to have Heads when she is interviewed, and 2/4 to have Tails.

Just waiting for the first guy to explain that 1/4 and 2/4 still are a third and two thirds since the interview actually takes place.