This answer has several parts.
First, you are misinterpreting Schrodinger. He is not denying that perception can come from matter, he explicitly leaves that open (nothing can be "discarded" yet, and no inference as to its ultimate source is yet valid either). Instead, he is just outlining the starting point for all our worldview IS our first-person and immediately experienced perceptions. The buildup of a "theory of the world" and "theory of other minds" is a complex inferential process, resting on this perceptual foundation. Whether identity theory, delusionism, or some other materialist view of mind can explain this process, or not, is still open.
Second -- YES, Schrodinger assumes that mind exists in this quote. For there to be "perception" there has to be a "perceiver". However, before running with this insight, hold for a bit. Thinking on the philosophy of mind has advanced a bit since Schrodinger's book, and so has the process of neurology, and its insights into our unconscious minds. It is better now to distinguish between experiencing, and perceiving. Perceiving is of SELECTED information, ORGANIZED and HIGHLIGHTED for our consciousness, by our unconscious minds. Our vision, for example, is not of the pixels that our eyes receive, but those pixels are grouped, using edge detection algorithms, and clumped into recognizable objects, and those objects are prioritized if they are moving, and particularly if they twig the "face" category, etc. For hearing -- continual background sounds are zeroed out for us, so that we can hear subtle changes, and baby/infant crying immediately catches our attention, etc. Here are two philosophic references that discusses the details of how our neural networked brains do information digestion for us. (See The Engine of Reason, the Seat of the Soul and Astonishing Hypothesis
The Scientific Search for the Soul.) These are both eliminative materialists, who try to dismiss the reality of consciousness, but their info on the nature of the UNconscious processing our brains do, prior to perceptions entering our conscious awareness, is highly relevant. As perceptions are highly post-processed, they have a higher theoretical, interpretive, and inferential content, and perceptions are not what you should be focusing on, as they are neither simple nor direct. Quales, in contrast, are what we experience. They are basically how our unconsciousness presents these digested perceptions to our consciousness. Some quales are experiential, others are organizational.
What this discussion shows is that perception, mind, and consciousness are not simple or non-equivocable terms. And doing reasoning with these sorts of unclarified terms, will likely lead to invalid reasoning. One should instead focus on quales and experience, as they explicitly require an experiencer. And also look at the creation of a theater by our unconscious mind, for our consciousness. These are the two clarified terms which can do some of the work you are hoping for to make an anti-physicalist argument.
Neither quales, nor this theater-producer/viewer relation between unconsciousness and consciousness, are comfortable concepts for materialist views of consciousness. And they are easily accommodated with an interactive dualist view. BUT -- this quote DOES NOT preclude that a physicalist model could be found that could work. As Quine noted, theory is ALWAYS underdetermined by evidence! So no it does not presume anti-physicalism. Nor does it presume causation for mind, nor irreducibility for quales.
However, according to Jaegwon Kim, the 50 years of philosophic investigation of reductionism and quales subsequent to Schrodinger's book have shown them to be irreducibly non-physical. (See Physicalism, or Something Near Enough) And evolutionarily thinking about consciousness readily shows that it must be causal. (See "William James and the Evolution of Consciousness".) But these are arguments which must be constructed, they are not obvious upon inspection from the quote. Combine then with the theater construction, and the experiencer, and you can make some progress in your project.
