mermaid
re your comments which I have separated out;-
"However, we do need to do something".
Actually you do not. That's your FOG talking there: fear obligation and guilt.
"We feel that the future for our relationship with our mother looks bleak".
Its already been bleak due to her overt narcissism and you are profoundly affected by her narcissism. I would suggest you read "Children of the Self Absorbed" written by Nina W Brown.
There is no future for you by having any sort of relationship with her, it is not possible to have any sort of relationship with a narcissist. All you can do is detach from her. This is and will not be at all easy for you because she (your mother) trained you well and from childhood.
"I am also very concerned for her as she moves into her old age. My dad is dead(although they divorced before he died), she is estranged from all of her close family and she is falling out with her friends and neighbours. Those who are in contact with her, appear to be limiting it and/ or "diluting" her company by inviting others to join them, which she really doesn't Iike"
And why are you so concerned about this?. Her behaviour is not your responsibility.
"I think the idea of picking a few things, focusing on these and then gently but relentlessly picking her up on them would work. I am very confident about my sister and I working as a team and communicate with each other".
Your sister and you should work as a team and support each other to detach further from your narcissistic mother. THAT is the only way forward here. I would suggest you read the website entitled daughters of narcissistic mothers.
"Has anyone else adopted this or a similar strategy with any kind of success?"
I have three narcs in the family, none of what you have suggested has or will actually work at all. Your life will be made ever more miserable indeed the longer you actually keep her at all in any part of your life.
"I have also noted how many people now have no contact and how positive you are about it. I don't feel like I am arc this stage yet and would like to try other things just now".
It is clear from your replies that you are not anywhere near being at the no contact stage yet but you probably will get there given time and a few more rebuffs from your mother.
It is NOT your fault she is the way she is; her own birth family did that lot of damage to her, they were the ones who put her on a pedestal and your mother has made the terrible choice not to love.
Encouraging her to see the GP is NOT, repeat NOT, a good idea at all. She will know more than the GP does and blame you again!.
Your boundaries re your mother are blurred as well. You need to reinforce those boundaries as of now.