This is simply wrong.
I'm not sure what "this" refers to. It can't be all that I wrote, because you agree that αἱρεσεις is the subject of τυγχάνουσι, and your rendition shows you think ἑαυταῖς and φανεραί are somehow joined by τυγχάνουσι just like I said they are. The heretics/heresies point is irrelevant here, that's why I gave a caveat about it, but frankly it can be translated to heretics (let's not start on that). The point of contention must be τυγχάνω+participle, and Ima talk about this shortly.
Is no support for you. It only shows that the verb may be used absolutely, probably with ἐοῦσα understood.
Then τυγχάνουσι here can be used "absolutely, probably with ἐοῦσαι understood" (whatever that means) too. Your point that it's no support for me doesn't stand. Nevertheless, bringing classical greek into a discussion of koine is hazardous, and I shouldn't have done it.
I showed why it was wrong and gave the proper reading.
If by proper reading you mean that truncated LSJ explanation, it's just a low-hanging cherry from the wrong tree (sorry), and saying that I'm wrong from that slim reading is quite a jump in conclusion — the most you can say is that you have some backing from LSJ. For the love of durians, Barry, pls exercise a bit of the principle of charity.
Now, τυγχάνω+participle... [pls wait a while for me to clean up the list of τυγχάνω's that I cobbled from Arianos]