I'm glad to hear that Jag is improving already.
Since you are already seeing regrowth of hair in the existing lesions, I don't think you really need the peroxide shampoo.
It can be helpful for resolution, but I think the quick response you are seeing with Jag is already quite positive.
I'm glad to hear that your kitties improved with the injection - other than ear mites I cannot think of another problem that would affect the ears of multiple cats at once!
I think your plan to have them checked for mites is perfect.
Amitraz dips are another method of treatment for the demodectic mange, but again, since the response to oral ivermectin is so good I do not think it necessary. If desired for faster resolution, it IS safe to use the amitraz and oral ivermectin at the same time.
Amitraz dips can be somewhat inconvenient though, as you must soak the dog and allow to air dry in the shade only.
Please let me know if you have other questions. I am happy to continue until I provide the service you seek.