That video doesn’t look like a typical allergy or parasite induced cough to me.
I know you probably feel like you’re hemorrhaging money right now, but have you considered having her throat scoped? Not trying to be an alarmist. She just sounds more like a horse with a throat/pharynx issue than a “respiratory” horse to me.
Side note: I’d definitely not blame the TC Senior, since the Gro 'N Win contains essentially the same ingredients, just in different proportions.