When n is large (like 300, even far less than 3000), the t-test is essentially the same as the z-test. That is, the t-test becomes nothing more than an application of the central limit theorem, which says that the MEAN for each of your two groups is almost exactly normally distributed (even if the observations underlying the two means are very far from being normally distributed!). This is also the reason that your typical t-table does not bother to show values for n greater than 1000 (for example, this t-table). Thus, I am not surprised to see that you are getting such well-behaved results.

Edit: I seem to have underestimated the extremity of the skewness and its importance. While my point above has merit in less extreme circumstances, for this question I would like to point out that I think whuber's answer to the question is much better.

When n is large (like 300, even far less than 3000), the t-test is essentially the same as the z-test. That is, the t-test becomes nothing more than an application of the central limit theorem, which says that the MEAN for each of your two groups is almost exactly normally distributed (even if the observations underlying the two means are very far from being normally distributed!). This is also the reason that your typical t-table does not bother to show values for n greater than 1000 (for example, this t-table). Thus, I am not surprised to see that you are getting such well-behaved results.

Edit: I seem to have underestimated the extremity of the skewness and its importance. While my point above has merit in less extreme circumstances, whuber's answer to the question is much better overall.

When n is large (like 300, even far less than 3000), the t-test is essentially the same as the z-test. That is, the t-test becomes nothing more than an application of the central limit theorem, which says that the MEAN for each of your two groups is almost exactly normally distributed (even if the observations underlying the two means are very far from being normally distributed!). This is also the reason that your typical t-table does not bother to show values for n greater than 1000 (for example, this t-table). Thus, I am not surprised to see that you are getting such well-behaved results.

When n is large (like 300, even far less than 3000), the t-test is essentially the same as the z-test. That is, the t-test becomes nothing more than an application of the central limit theorem, which says that the MEAN for each of your two groups is almost exactly normally distributed (even if the observations underlying the two means are very far from being normally distributed!). This is also the reason that your typical t-table does not bother to show values for n greater than 1000 (for example, this t-table). Thus, I am not surprised to see that you are getting such well-behaved results.

Edit: I seem to have underestimated the extremity of the skewness and its importance. While my point above has merit in less extreme circumstances, for this question I would like to point out that I think whuber's answer to the question is much better.