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This won't be all that helpful, but I know that ἔχω + aor. participle is used as a substitute for the perfect (at least in Sophocles), although I was under the impression it was only used with active participles, but I'm probably wrong on that. Then I guess π?οσδ?ακεῖν would govern ἔχειν, but that looks odd to me because I would expect a participle here instead of an infinitive, but maybe I'm missing something here.
Going off your translation, I would say something like
"It is at hand for me to see the navel of the world gain a terrible curse of blood to have."
Basically I took ἔχειν to be a final infinitive to mean that the navel will continue to have this curse on it. So I took ά?όμενον to be the object of π?οσδ?ακεῖν.
How would the infinitive function in your translation? it seems to me the the middle participle "aromenon" is functioning as an active verb in this sentence and hence could take the periphrastic construction with exein.
In my translation, it functions as an infinitive of purpose/result (more the latter than the former considering the context). The significant difference between your translation and mine is that in yours it's the fact that the curse has been acquired that is beheld, while in mine it the acquisition that is being beheld, so perhaps the larger context could decide which interpretation fits best.
About the periphrastic construction, I looked through what I have and I'm no wiser about whether this construction actually does require the active or not, so as far I can see it, it's certainly possible. The bigger problem for me is having π?οσδ?ακεῑν take an infinitive instead of a participle, since it seems to me the participal construction is what you'd expect with verbs of perception. On the other hand, I could very well be wrong, and reading ἀ?όμενον ἔχειν as "have gained" makes perfect sense.
I think you are correct that "prosdrakein" does not take the infinitive; however, I just looked over the uses of the infinitive of purpose, and it just does not seem to fit in this sentence. Could it be an infinitive of result, expressing the result of the participle "aromenon," that the navel of the world has gained this curse with the result that it must now possess it forever?