The commentary in Perseus say that οἷς is equivalent to τούτοις ἅ, of which ἅ is obj. of ἐπίστασαι and τούτοις modifies ἁλόντα. Fair enough, but I also can’t help but think that αὐτὸν ἁλόντα is a complementary participle to ἐπίστασαι and so wouldn’t that mean ἐπίστασαι would have two objects ? (ἅ and αὐτὸν ἁλόντα) I’m assuming οἴομαι is parenthetical and isn’t modifying and περὶ πολλοῦ ποιεῖσθαί σε is an epexygetical infinitive.
The gist is something like… You yourself know the things, I suppose, which would win him over, making him value you greatly.
I take περὶ πολλοῦ ποιεῖσθαί σε as the infinitive in an acc.&inf. construction. As I read it, the skeletal structure within the relative clause is ἐπίστασαι … ἂν αὐτὸν … περὶ πολλοῦ ποιεῖσθαί σε, “You know that he would value you.” Admittedly acc.&inf. is unusual with επίσταμαι.
ἁλόντα I take as subordinate to the infinitive (so lit. “that he, having been caught, would value you”).
As for the relative itself, the way I read the Greek, οἷς incorporates another object of μηχανᾶσθαι, so that the sense is “but (the things) by which you yourself know that he …”. In other words, I take οἷς as “equivalent” not to τούτοις ἅ but rather to ταῦτα οἶς (though I deplore this kind of formulation). Apparently this is different from the commentary you cite.
So syntactically I’d say we can reduce the whole thing to οὐδέν γε ποικίλον … δεῖ … μηχανᾶσθαι, οἷς δὲ … ἐπίστασαι … ἂν αὐτὸν … περὶ πολλοῦ ποιεῖσθαί σε. (“… must contrive nothing fancy but just the means by which …”).