The reason you can’t invite a non-jew on Yom Tov is because you might add more food thereby increasing the cooking even though you are allowed to cook for a Jew. So if you transferred the food to the non Jew prior to Yom Tov you will not be cooking more food for him.
I think the home health aide is similar to a Non-Jewish spouse in that it’s a package deal if you invite the family you must include the spouse, so to if you invite the senior you need to have the health aide also. Although, I have seen many health aides hanging outside while the family is eating the Shabbos meal.