As I understand it, there are a number of alternatives to pantheism. Panentheism, in which the sum is more than the totality of the parts; theism, in which the totality moves the parts but not vice versa; polytheism, in which there is no one overarching totality rather a multiplicity of near- or quasi-totalities; henotheism, in which the totality is refracted in a multiple of hypostases or avatars; atheism, in which the totality, if there is one, is not an agent; and so on.
Zarathushtra broke aggressively with polytheism and panentheism requires dualism of which there is no trace before Egyptian agricultural feudalism and certainly not in Central Asia 3,700 years ago. So logically you will have to remove all alternatives until you end up with monist monotheism. None of the others apply to the Gathic author.
To say that it is up to the questioner to demonstrate that Zarathushtra was not a monist doesn't strike me as intellectually honest.
To say that somebody is intellectually dishonest strikes me as being intellectually dishonest in itself. Back to you: Where do you find any traces of dualism in The Gathas, centuries before such ideas developed in a very different part of the world?
One cannot prove a negative. If there are passages in the Gathas which may be read monistically or pantheistically, we should be able to identify them.
Not necessarily. You need to KNOW within which society a certain text was produced. For example: You would not ask me to prove that America does not exist in a European text from the 12th century because you KNOW that America was discovered by Europeans in the late 15th century. To still debate whether America as a continent is a conscious phenomenon with 12th century authors is fruitless if not outright idiotic. How could dualism possibly serve what Zarathushtra tried to communicate? It serves no role whatsoever within his ethical system.
Also, you say that Zarathushtra precedes Judaism by at least 700 years. What are you using for a start date for Judaism?
King David is the first know historically existent person in Judaism so Judaism as Judaism would have developed some decades before King David steps onto the historical scene. There are for example not a shred of evidence that Abraham or Moses ever existed, we have to refer to them as mythological creatures. As we have to with Judaism before the exile in Babylon where the faith was properly developed.