This is also very good. I like the choice of nullus. A couple of quibbles, the first of which I'm more sure about than the second:
neque can't be postpositive...it doesn't have the usual word order freedom, it needs to be before whatever it's negating and joining.
(less sure on this one) insuper is an adverb rather than an adjective, so it can't be used as a predicate for the noun nihilum. The public-domain dictionary I checked Lewis' An Elementary Latin Dictionary has it as a qualifier for the verb in all three of the citations it gives for the relevant sense.
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.
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.