On exclusion as the meaning of a word (Apoha in Dharmottara)

I could finally read Kei Kataoka's critical edition of Jayanta Bhaṭṭa's Nyāyamañjarī section on apoha. The critical edition is preceded by a long and insightful study on the theory of apoha as depicted by a Jayanta (a Nyāya author of the X c.). The study opens with a "survey of research", which I very much appreciated (see an older post of mine on the necessity of being aware of previous results), also because it makes some results of the japanese scholarship available to non-japanese readers. Jayanta distinguishes three theories of apoha, roughly corresponding to Dignāga's, Dharmakīrti's and Dharmottara's ones. Dignāga depicted apoha as the absence of anything else. Hence, the meaning of "cow" would have been just the exclusion of non-cows. But Kumārila criticised this view insofar as a non non-cow closely resembles a cow (!). Hence, Dharmakīrti stated that apoha is not an external entity (such as the non non-cow mentioned above), but rather a part of the cognition itself. This, again, may be problematic, since then there would be no distinction between what is grasped through a word (a part of cognition conveying the meaning "cow" through the exclusion of non-cows) and what is grasped through intellectual perception (a part of cognition assuming the form of a universal, such as 'cow').

Therefore (if I am not misunderstanding Kataoka's point), Dharmottara concluded that apoha is neither external nor internal (nāyam āntaro na bāhyaḥ). Does this mean that, since it is unreal, it cannot be external (and since it is not part of the cognition, it is not internal)?

This apoha is, follows Dharmottara, only super-imposed (āropita) and is not real in any sense (neither as absence –as with Dignāga– nor as part of the cognition –as with Dharmakīrti). But since there is no subject and since the apoha is not part of the cognition, how does this super-imposition occur? Because of residual impressions (vāsanās)?

Dharmottara further specifies it as vyāvṛttichāyā ("shadow of exclusion" or "exclusion as shadow") and as dṛṣyachāyā ("shadow of the perceptible entity"). I am not sure about the translation of the first term and about the interpretation of the second one. Whose shadow is it? How can it be without any support (neither external nor internal), but still able to have a practical efficacy (arthakriyā)?