Since you have a large sample size, even small deviations from normality can give a small p-value.  From what you said in comments (which should have been edited into the post) about the purpose, that the upper tail is of interest while the lower, where the largest discrepancies can be found, is not, you could well base your work here on the normal assumption. That conclusion is corroborated by @whuber's calculations in comments.  

See also https://stats.stackexchange.com/questions/2492/is-normality-testing-essentially-useless