I did try the soapy water on the thyme just after I took those pictures, but now, thank goodness, it is raining! And of course that's washing off the soapy water, whatever might have been left. I may not have enough soap in there, either.
If this continues to spread, I'll try the baking soda. That's a new one on me.
I'm not going to concern myself with the mint, it's too complicated and she's not worried about it, so I'm not going to bother.
My theory of the day is, whatever is going after these herb leaves is doing so precisely because they are concentrated. The bugs need the nourishment?
Makes as much sense as anything else.