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 Is normality testing 'essentially useless'?
More generally, formal statistical tests are not that helpful in judging qq-plots. Visualization, like simulated (or calculated) confidence bands, and other methods like presenting a multi-panel plot with your qq-plot together with many simulated ones, are more helpful. Examples and discussion at Interpreting QQplot - Is there any rule of thumb to decide for non-normality?
