What is your mother like normally? Or, how was your relationship with her before you came out? I ask because that seems like a fairly extreme reaction, but if she is usually angry and verbally abusive then it's hard to see how you can work through that kind of defence mechanism. If she usually isn't (or wasn't before you came out) then maybe you have something to work with.
I don't know how you define offering the olive branch, if it is a passive "hope she comes to her senses" or if there is a degree of direct action involved from you.
For me, my father was very resistant to my transition. He is also in his 70s. Fortunately he was never prone to tirades or hateful words and I never copped an earful when I initially came out to him. However he was in no hurry to meet me after I transitioned, he clearly didn't agree with my decision, didn't understand and didn't want to talk about it. His few emails to me continued to address me as [deadname]. Still, I proffered the olive branch, I wasn't going to push him or demand anything but made it clear I was willing to meet and discuss when he was ready.
Then, out of nowhere I got an angry email from him making all sorts of bizarre accusations. It was hurtful and made me see red. I wrote an immediate angry reply but never sent it. Once I cooled down I retooled the reply, made it respectful but at the same time made it clear in no uncertain terms that the accusations were incorrect, that I was who I was, that I would not tolerate being called [deadname], that I was happier in my life than I had ever been...and I re-offered the olive branch. (I wrote about it at the time here in the forum.) There was radio silence, then he had to go into hospital/physical rehab (something unrelated!) and a few months later I got an apologetic email from him. He still doesn't call me Grace but at least he doesn't call me [deadname] either...a middle ground I'm prepared to accept.
I guess what I'm saying, in my father's case I had offered the olive branch but was prepared to switch to iron fist when that was what the situation called for. But that was keyed directly to him and his psychology. I don't know whether being more assertive and direct with your mother would work or would only inflame her further.
It can be terrifying to confront our parents. My father is at least semi reasonable and reflective of his behaviour, but I was still afraid to confront him the way I did. Relationships with parents are difficult. Even when we are adults they still hold a certain sway or power over us that we normally would never invest in anyone else. Dealing with them means knowing them and knowing your relationship dynamic with them knowing their defensive tactics and knowing how to find a way through that. There is most likely a way through to your mother but it may require a bit of "iron fist" as well as olive branch.