I keep looking back at this one and am convinced that you were right on with your own suggestion of "ceremonial nature." I really feel like it's the one word that captures the neutral tone of the source text (as opposed to terms that might carry a slightly negative connotation), while also being a word generally associated with spirituality.

This option keeps you from having to add on translation of "...einer Zeremonie," which could become distracting (as Craig has pointed out), since the focus of the sentence is on the rituals (not a ceremony, as such). Some might consider this undertranslating, but I am quite certain that the full meaning (including the "überhöht") is present in the English term.