>you could construct a synthetic reality for that brain that it would not be able to distinguish from its previous brain-in-a-body experiences.
No. I'd recommend reading Dennett's Consciousness Explained for a longer treatment of this, but if you want to have an experience just like you, you need a body and an environment just like you. Sure it could be synthetic in the sense of it being artificially constructed, you could have artificial limbs, but it can be no different from the one you have, it cannot be a vat. There is no "Cartesian Theater" in the brain, your experience is already distributed throughout both your brain and body. Your experience isn't something being "fed into you" (the brain) from the outside, the entire perception emerges in the first place through being embodied in the world. The concept of the thought experiment itself would not even make sense without implicitly assuming an embodied reality beforehand setting it up.
Just like there is no philosophical zombie that's somehow materially identical but without sentience, the reverse doesn't exist either. There is no disembodied computer with the experiences of an organic being because they function in entirely different ways.