Roughly how large would me sample size have to be to reduce the importance of normality?

50 or so.

I have ~6500 observations

Well...if you performed formal tests of significance in order to decide

whether your residuals are (non-)normal, then with this sample size

the power of such tests is absolutely extremely much much too high.

But maybe you used graphical methods (histograms, Q-Q plots...)?

Anyway, results shouldn't be affected by the shape of the residual

distribution with such a large sample size, I suppose.

This depends on how you gathered your data. If you e.g. had 3 insects

which delivered 2160 data points each, then things might be different.

With kind regards

K.