It sounds like everyone is still relatively new to dealing with polyamory. Add to that communication over emails that don't work welll for people and I can understand your problem.
One thing I have learned is to tell people that I am very literal and logical. Sometimes people try to read what you mean by the wording you use or what was not said. I see that leading to miscommunication because a lot of assumptions are made.
One of the toughest parts of polyamory is learning how to communicate in an open way that gets your point across. It means that people have to be honest with themselves; know what they want; and be open to other people. It is too easy to get defensive or go passive aggressive.
It sounds like J was still trying to come to terms with polyamory to an extent. She was probably still feeling like you may be competition so talking about labels may have come across to her as seeing about the odds of you replacing or becoming more important than her. Yet on an intellectual, she may have realized that this is probably not happening. So this usually leads to confusion.
My advise would be to take is slow with them if you want to continue trying. Keep things at friendly banter and talk about it becoming more serious later on. I think polyamory could work for you, but it may work better with someone more experienced.