I need to determine which variables have the greatest relative impact. Note that some suggest beta weights but others reject this for dummy variables or when you have variables that are not normally distributed (and I will always have some).

they suggest this

It is more sensible to estimate the change in Y when X is changed by an amount that is subject matter relevant. For binary predictors this is the change from 0 to 1.

For many continuous predictors the interquartile range is a reasonable default choice. If the .25 and .75 quantiles of X are g and h, linearity holds and the estimated coefficient of X is b; b X(h-g) is the effect of increasing X by h-q units which is a span that contains half of the sample of x.

Are they saying you compare the slopes of the dummy variables to the slope of an X for the IQR and which is relatively larger would have the greatest impact. I am not entirely sure how to set the X to the IQR to run those slopes. You just make every X equal to the IQR of the variable?