Another vote for sudocrem/ Vaseline here. I try to limit rubbing on our pony by having a 'slimming paddock' for one day and then turning out with the muzzle of shame on the next day.
I have found binding the offending part of the muzzle in gaffa tape to make it smooth helps too.
I'd put a bit of sudocreme on it and move the muzzle a fraction by lengthening or shortening the straps just a little bit so it doesn't continue to rub on the same bit.I use a dinky muzzle and find it is well padded and doesn't rub.
I wrap all the plastic bits on a Greenguard in Vetwrap. It stays on all summer and prevents rubbing despite getting a bit grotty looking. If any rubs, smear in sudocrem.
Get rid of the muzzle and put on restricted grazing and/or bring in for part of the day. Supplement with soaked hay. Increase excercise to help control weight gain.
Sudocreme will help keep flies off and stop it getting infected.
Awful things!! Sorry!