"Forgive me, but I find this difficult to believe. In a quasi-impersonal the infinitive subject does not seem to me to require a further subject."
Well, don't believe it, then. But how do you explain τηλικοῦτον ὄντα? Why is τηλικοῦτον ὄντα accusative? It can't be the direct object of ἀγανακτεῖν, because ἀγανακτεῖν is intransitive.http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.04.0057%3Aentry%3Da%29ganakte%2Fw
If Plato had inserted a personal pronoun, it would probably have been μοι, as what Smyth calls the "dative of relation" (sec. 1496), with the impersonal expression πλημμελὲς εἴη. But the person who would be vexed is Socrates, i.e., me, the implied accusative subject of ἀγανακτεῖν. And that's why τηλικοῦτον ὄντα is accusative--because it agrees with the implied accusative subject of the infinitive ἀγανακτεῖν.
I think you're confused by Smyth's description of δεῖ as "to go binds me." This isn't δεῖ. Smyth lists other "quasi-impersonal" verbs such as πρέπει, προσήκει.http://www.perseus.tufts.edu/hopper/text?doc=Smyth+grammar+933&fromdoc=Perseus%3Atext%3A1999.04.0007