To me, it seems clear that there is a continuum between this group of sounds, as all of them (apart from ç, which I will touch on later in the post) are sibilants, and the only difference between them is in the place of articulation. However, when I try to analyse the differences in place of articulation, a one-dimensional continuum doesn't appear to form, as the position of both the blade and the middle of the tongue varies throughout the group. This is counterintuitive to me, as I can intuitively describe the progression s-sʲ-ç-ɕ as a simple continuous softening of the sound "s", with each subsequent element being a softer version of "s" than the last, and the progression ç-ɕ-ʃ-ʂ as a simple continuous hardening of "ʂ", with each subsequent element being a harder version of "ʂ" than the last. Furthermore, historical phonological changes such as s-->sʲ-->ɕ-->ʂ in Russian second-person singular ending -шь reinforce this intuition.
Similar progressions are z-zʲ-ʝ-ʑ-ʒ-ʐ, t(s)-t(s)ʲ-c-tɕ-tʃ-tʂ, d(z)-d(z)ʲ-ɟ-dʑ-dʒ-dʐ, and possibly even ɳ-n-nʲ-ɲ and ɫ-l-lʲ-ʎ.
I shall note that, in all of these progressions, the "bridge element" is always a palatal consonant which is functionally different from the rest of the group: ç is the only non-sibilant in the group and can be analysed as an advanced x; c is the only non-affricate and can be analysed as an advanced k; etc.
In light of all of that, here is my question: are the qualitative differences in the group s-sʲ-ç-ɕ-ʃ-ʂ and similar groups described above attributable to a single phonetic process? If so, what is that process? Additionally, why do the palatal consonants not fit in phonetically despite fitting in perfectly qualitatively?