Neque: you're right about this one. I was sure I had seen 'neque nec' used contiguously, but I must have misremembered as I can't find an example of that. Fixed.
I know "insuper" is an adverb; it works here just like "above" (which is also an adverb) does in English, i.e. they predicate an implicit verb "est / to be". EDIT: Just to be safe, I quickly checked the medieval dictionary I linked before, and it has plenty of instances of 'insuper' with ellipses of the verb.
Thanks for the link, that's a very nice medieval resource. I agree now that insuper here is okay, there were a couple of uses very much like yours. Interestingly, it seems that in the majority of those medieval citations, insuper wasn't related to location or being used as an adverb at all...it was being used more often as a preposition (with accusative) meaning "beyond" or "in addition to".
If anyone can do non-wrong Latin, I could use a translation of the following for HPMOR. The original is supposed to be circa 1200.
No rescuer hath the rescuer.
No Lord hath the champion,
no mother and no father,
only nothingness above.