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The connection between Hinduism and the idea that everything is a construction of the mind is very interesting. You say that Hinduism shows that everything is not a construction of the mind, and your argument is compelling. Though perhaps one can make the opposite argument in the following way. According to Hinduism, our ordinary perception of the world is an illusion (maya). Ordinarily our perceptions suggest that in the world objectively there is duality and multiplicity; I see that I am not the table or that the table is not the chair. But our ordinary perceptions are mistaken because there is no duality in the world; there is only oneness. So our ordinary perceptions are not objective and are only constructions of the mind which creates a sense of duality when in fact there is no such duality. On this argument, it is the overall oneness of the world which suggests that everything we normally see is actually a construction of the mind. I think it is very thought provoking how one can draw from the same premise (the oneness of the world or the universal self) different conclusions ( that the world is a construction of the mind as the above argument suggests, and that it isn't, as your argument suggests.)