I was made a mod over the weekend.
I've been waiting for a good lead-in to post more photos. Your comment about switching to an armbar was just what I was waiting for.
So you're going for the choke like normal and have trapped their far arm.
But for some reason the choke isn't working. In this case, it's because I'm reaching up and trying to pull the elbow up and out from behind my head.
Release the knee and trap the arm. You need to have this arm or his knee controlled to prevent him from turning away.
Bring your arm to the other side of the head, pass your leg over and finish with an armbar. If they defend this, you can just take their back again and return to the choke.
You can also often switch to the single wing choke.
Same situation, they're trying to pull your choking arm off.
I release the knee and reach under the arm.
I finish with a single wing choke by straightening my arms.