There wouldn't be a property dispute if the mother church hadn't abandoned its own teachings.
I cannot confirm this, but I can tell you a story from late 2003, when we were still in ECUSA but preparing to pull up stakes. We were visiting around, and I called the Anglo Catholic parish on the other side of town to see about when services, choir practice, etc. were scheduled. The receptionist gave her name when she answered the phone, and it sort of registered as familiar in a vague way. We chatted, and I asked some questions about the parish. I thought her answers were strange - when I asked about whether the parish was high or low, she responded, "Oh, everybody over here has about the same political opinion," in a really snarky tone. But I went with the flow and thanked her and went on my way.
The next Sunday, I'm lined up with the choir waiting to go in when I belatedly remembered where I'd heard the receptionist's name before -- she was one of our vestry members, and she was standing right there with the vicar (an ex-Jesuit priest who quit the RCs to get married). So I took the bull by the horns (I already knew we weren't staying), and said, "Didn't I see you over at Our Saviour?" She and the parochial vicar both started laughing, very loudly and inappropriately.
I'm pretty darned sure she was sent over there by our rector to spy on poor Fr. Tanghe, probably at the direction of the bishop.
I am SO glad I am out of that snake pit that calls itself a church . . .
Traditional Anglican ping, continued in memory of its founder Arlin Adams.