If I wire a pink unicorn detector up to an invisible unicorn detector such that a light goes on iff both detectors fire on the same object, have I not just constructed an invisible-pink-unicorn detector?

Maybe. Or maybe you've constructed a square-circle detector; no experiment would let you tell the difference, no?

I think the way around this is some notion of which kind of counterfactuals are valid and which aren't. I've seen posts here (and need to read more) about evaluating these counterfactuals via surgery on causal graphs. But while I can see how such reasoning would work an object that exists in a different possible world (i.e. a "contingently nonexistent" object) I don't (yet?) see how to apply it to a logically impossible ("necessarily nonexistent") object. Is there a good notion available that can say one counterfactuals involving such things is more valid than another?