Good additions, faye.
I'm guessing that what you call pelham roundings are what we call in the US a pelham converter? A horrible device that essentially turns a pelham into a kimberwicke and allows you to ride with a single rein?
I like your #3, and would like to add #4 - in the Southeastern US, some horses are inordinately bothered by small insects, both in their nostrils and ears. So an ear net, and is some cases a muzzle net should be tried to rule out that cause of head tossing as well.