I've resisted the rendering "sophisticated [stuff]" for τὰ σοφά, but can do so no longer (Beresford in the Penguin has "sophisticated knowledge"). Hippocrates' comment "as the name implies" doesn't make much sense in English without the etymological argument being brought out, and a bit of looseness seems acceptable to get the point across to the Greekless reader.

I've also changed the (οὐκ)έτι in the last line of section e from "any more" to the more perspicuous "this time". Jowett fails to translate the word altogether, but it marks an important point: Hippocrates can answer Socrates' questions about the music teacher and the painter, but not about the sophist. "Any more" might suggest that he once had an answer to this question, but even though he did purport to know what the sophist was above in section c, it's not plausible to think that he had in mind an answer to Socrates' more specific question about the content of the sophist's knowledge. So it makes better sense to take the contrast implied in οὐκέτι to be with the preceding examples.

(1) ὦ νεανίσκε, ἔσται τοίνυν σοι, ἐὰν ἐμοὶ συνῇς, ᾗ ἂν ἡμέρᾳ ἐμοὶ συγγένῃ, ἀπιέναι οἴκαδε βελτίονι γεγονότι, καὶ ἐν τῇ ὑστεραίᾳ ταὐτὰ ταῦτα

(2.i) εἰ […] ἀκούσειεν αὐτοῦ ταὐτὰ ταῦτα ἅπερ σοῦ
(2.ii) ἀκούσας ἐκείνου ταὐτὰ ταῦτα ἅπερ σοῦ

In (1), the ταῦτα is vague and picks up on the whole preceding sentence from ἔσται to γεγονότι. 'The same thing' seemed idiomatic (it captures Protagoras' elliptical syntax) and sufficiently emphatic, since the ταῦτα is just clarifying what the ταὐτὰ refers to, namely, Protagoras' claim that Hippocrates will improve in his company.
In (2), the ταῦτα is correlative with the ἅπερ that follows, which is why it makes more sense to translate with 'the' instead of 'these'. The ταῦτα isn't especially emphatic; it's just pointing forward to the relative clause.

1. I like 'getting nowhere with' for ἀπορίᾳ, but I'm not sure that captures both Prometheus' intellectual frustration and his practical desperation (LSJ catalogues both senses) which goes with the extremity of P's eventual solution. I suggest 'at his wits' end'.

2. The article in 'the technical knowledge' sounds a little odd.

3. I'm not sure about 'save' for σωτηρία without a further 'from…' in a non-Christian context. Something like 'protect' might be better. I'd use 'Hephaestus', but I suppose it's for you to choose.

'personal discoveries' - sounds a bit odd, because reminiscent of 'personal development'

'go on' - not the meaning of διεξιέναι ('explain'; 'expound')

ἦν γάρ ποτε χρόνος - you haven't translated the γάρ (He's said he's going to tell a story; and the γάρ means 'so here it is')

These are tiny, tiny quibbles.

There's a reference to 331e's dE toi in Denniston (p. 552). He suggests embarassment: "Well, you know, they call him a sophist …"

Good luck,
Cathal

On your other important point, re: πολιτικὴ τέχνη, you're absolutely right that something to do with citizens often better gives a better sense for πολιτική, as here. Readers will have to pick up on the important, but separate point, that being a good citizen, on both Socrates' and Protagoras' accounts, involves being good in one's own private life and as an active participant in affairs of state.

I've made various other minor changes, as you and Nakul have suggested:

Nakul, does this work better for ἦ καλόν τέχνημα ἄρα κέκτησαι, εἴπερ κέκτησαι? "Well, you certainly have a nice trick up your sleeve … if you have it."