I like these plots.
The model "orange" line shape looks an awful lot like the linear BS ATM straddle price for small DTE, i.e., proportional to sqrt(DTE)
Also, in that small DTE BS ATM model approximation, straddle RV is proportional to IV*sqrt(DTE)
I don't suppose you have looked at how closely your model line is to sqrt(DTE)?
So my interpretation is that the blue line separation shows resistance to the sqrt(DTE) time decay, for certain time periods before earnings, correct?
What would happen if you tried normalizing the blue historical lines with 1/sqrt(DTE)?