νησιώτας δὲ τί δοκέεις εὔχεσθαι ἄλλο ἤ, ἐπείτε τάχιστα ἐπύθοντό σε μέλλοντα ἐπὶ σφίσι ναυπηγέεσθαι νέας, λαβεῖν ἀρώμενοι Λυδούς ἐν θαλάσσῃ, ἵνα ὓπερ τῶν ἐν τῇ ἠπείρῳ οἰκημένων Ἑλλήνων τίσωνταί σε, τοὺς σὺ δουλώσας ἔχεις;’
This is the closest I can get (with no attempt to put it into natural English):
And what do you expect the islanders to long for other than, (as soon as they learn [that] you are intending against them to build ships) to catch [the islanders] praying the Lydians in the sea, in order to, on the behalf of those mainland living Greeks, [i.e.] those you having enslaved hold.
(The bits in square brackets in the translation are where I've put stuff in that seem to me to be strongly implied by the Greek but not explicit)
It's the orange highlighted participle that puzzles me. I can't work it in to the rest of the sentence. What does it add to the meaning?