Nhanda saves possession

Today I picked up my Nhanda grammar at random with the intention of trying to find incompatibilities with Koa. The page I opened the book to just happened to describe nominal derivation, specifically the comitative and privative suffixes. A few samples:

nyarlu abarla-waa

woman child-COM

"the woman is pregnant"

ardu-tha apa-waa

spouse-my water-COM

"my husband is drunk"

thudu mindinyu-waa

meat maggot-COM

"the meat has maggots"

yatka-nu nguutu-waa

go-PIMPF horse-COM

"he went away on horseback"

ngayi ardu-nyida

1SG spouse-PRIV

"I haven't got a sweetheart"

wilu-nggu apa-nyida

river-LOC water-PRIV

"there's no water in the river"

I marveled for a bit at the examples and was about to put the book down when it struck me: first of all, Koa me can be used for all sorts of things I wasn't really thinking about, and I should clearly be thinking of it as a comitative case particle (or Turkish -li) rather than simple "with"; but most crucially, I've been having such trouble with semantics in possessive clauses in Koa because I've been doing it backwards.

Using me as my particle of possession, I was constructing phrases like a sene i me ni on a Russian/Finnish/Welsh/etc. model. They drove me crazy with aesthetic dislike: the particle with sene is clearly wrong but there's nothing to replace it with; why is "is with me" the predicate here, when clearly it's the cat that should be in that spotlight? All of this goes away when I do it like Nhanda, whether the clause is affirmative, negative or interrogative:

ni me sene

1SG COM cat

"I have a cat"

ta na me sene

3SG NEG COM cat

"he doesn't have a cat"

ei se me sene?

QU 2SG COM cat

"do you have a cat?"

It's perfect, and I'm almost embarrassed not to have thought of this before: marking the dependent instead of the head. In this way me sene becomes a flexible compound predicate like any other, giving us ti mehe me sene "that guy with the cat," etc. (lit. "that guy who has a cat" -- clearly if the cat is a specific one that's on the stage already, it would be ti mehe me ka sene)

Having me available for use in this way also reaffirms my thought that it can be used as an instrumental (ta si mene me tupo "he went on horseback") and adds that great Turkish -li functionality: a talo me asa "house full of spiders," "spider-having house." What a coo. I'm almost giddy with excitement.

A question, then: since we've got -li, what about -siz? Do we have a privative particle, or make do with na me? I was playing around with no for this, a kind of inside joke; here's how they would compare:

ti soe i na me kala

SPEC river 3SG NEG COM fish

"that river has no fish"; "there are no fish in that river"

ti soe i no kala

SPEC river 3SG PRIV fish

"idem"

Or turning to our ever-popular possession of cats, manifestly a crucial matter to be able to discuss:

ni na me sene

1SG NEG COM cat

"I don't have a cat"

ni no sene

1SG PRIV cat

"idem"

Used adjectivally:

a talo na me ko loha

INDEF house NEG COM SPEC love

"a loveless house"

a talo no ko loha

INDEF house PRIV SPEC love

"idem"

I'm sort of surprised to be liking the na me sentences more. I wonder if it's because I'm not used to having this kind of privative machinery at work in the primarily IE languages of my deeper acquaintance, or a dislike for the chosen particle (do these improve as, for example, ti soe i lo kala, ni lo sene, a talo lo ko loha?). I should think about this, because I rather think it would be nice to have a separate morpheme for "without" rather than just na me.

Or maybe that's just IE stubbornness.