Khazar (and also Yemen Jewish state in about 10th century) is an interesting example – if this were controversial, there should be some discussion of shevuos at the time.
I think the weak spot in this discussion is that there are very limited sources on both sides – as the issue was not “hot” for centuries. So, it is worth looking at the times and halachik sources that discuss relevant issues – and if they skip over the issue of shevuos, what are the implications?