The general AI I described would have self-reflection, agency and arguably consciousness, yet - per orthogonality thesis - it may not have anything resembling human values.
Sorry, but I don't think you have any rational basis for imagining what the "space of possible minds" represents. The only minds with human-level intelligence we know of are human minds that have (with variation) human values.
The claim you're making is analogous to saying "any extraterrestrial life we find won't be carbon-based because out of the space of all possible substrates for life, carbon is a very particular one", but that's an ill-founded supposition because we have a sample of N=1 and maybe carbon-based life is the only kind of life there is.
Maybe a true GAI mind will be "like us", maybe it won't be, but we don't have anywhere near enough data to speak with confidence about it.
Is that really "general" intelligence, then? I would argue we don't know today whether consciousness and agency are separable from general intelligence. You could say that "general intelligence" implies some degree of intelligence on any topic, which would include self-reflection and metacognition.
It sounds to me like you're describing something like a p-zombie[0], which we don't know to be able to exist.
[0] https://en.wikipedia.org/wiki/Philosophical_zombie