I think you misunderstood what I said or I didn't explain myself well: I'm not assuming that the DALY distribution obtained if you choose interventions at random is normal. I'm assuming that for each intervention, the DALY distribution it produces is normal, with an intervention-dependent mean and variance.

I think that for the kind of interventions that GiveWell considers, this is a reasonable assumption: if the number of DALYs produced by each intervention is the result of a sum of many roughly independent variables (e.g. DALYs gained by helping Alice, DALYs gained by helping Bob, etc.) the total should be approximately normally distributed, due to the central limit theorem.

For other types of interventions, e.g. whether to fund a research project, you may want to use a more general family of distributions that allows non-zero skewness (e.g. skew-normal distributions), but as long as the distribution is light-tailed and you don't use extreme values for the parameters, you would not run into Pascal's Mugging issues.