Ok, I have the same problem with midges on my Black Welsh Mountains, and yes they will kick their bellies raw too. And armpits. And rub their face raw.
Crovect will put the midges off for a while (make sure you put some up their neck), but you would have to keep reapplying it every 6 weeks say. That's not something I want to do. Stockholm tar works very well, but a) its sticky, messy and the smell lingers on you for days, and b) you will have to do that every week.
The option that I have gone for is to cull. I have had this problem for a few years and have noticed that it is hereditary. So anything that gets scabby ears or worse goes for the freezer. Sorry. it's like in people, some folks are more tasty to midges than others. I think also, some black sheep can have a more allergic reaction to midges too. And thus, its not fair on the sheep to propagate that trait.
For now I would treat with stockholm tar.
Also, for info, mine seem to get it worse in April/May and then again in August/Sept.