I think you handled this well, both the initial letter and the response to her response. You were honest and clear and polite. I am really sorry she's not willing......especially when you genuinely feel the need for it and don't feel like whatever you did discuss really was like closure.....{hugs}
I have been through something similar. Last summer, my T thought she wasn't helping anymore because I was in a major breakdown, not getting better, so she said in a month she would refer me but if there had been improvement she would re-evaluate at that time. Well, I ended up getting taken to the hosp by the police () while she was on vacay and when she got back I was still there and she terminated me....yeah, we had talked about the whole thing of her referring me for a little bit, but how was that supposed to be closure? A 10 minute phone conversation while I was in the hosp....then I left town, had another T there. When I was going to come back home, that T thought a closure visit would be helpful for me.....xT acted willing, but 3 weeks went by with nothing.....2nd T thot I should call her, so I did, but it ended up that 1st T called 2nd T and asked her to explain a thing or 2 to me.....so I didn't get a closure session either, or what felt like real closure. So I wrote a fat long letter.....it helped.....but occasionally I have found myself reminded of something and I get really furious or really sad all over again....grrrr.
As 2nd T said, sometimes relationships just don't end well, we don't get the closure we want from that person, and we have to accept it, deal with it the best we can and let go.....so here I am, not really with a T at the moment, doing the processing/letting go/grieving process.
It's not easy and I am sorry you have to go through it, and I hope your current T can help you with processing the relationship with xT and how it went/ended.....