I've just started having these conversations with my mom, because her mom just passed away at 99.
My mom isn't as temperamental as you're describing, but she doesn't like talking about death. However cleaning out her mom's old condo has forced her to think about it, and that's the lens of the conversations.
It's not going to be one conversation, btw. I think that's the key thing to understand: you're not trying to figure out how to talk to them about end of life planning one time, you're trying to figure out how to talk to them about full-life planning maturely from now on.
I would focus on specific issues rather then a broad concept; relate it to things that others are going through as a reference point; discuss it through the lens of ensuring a long, dignified life instead of about the end part; and try to offer appealing solutions rather than problems that they need to solve.
For instance, 'I was just talking to a friend who was visiting their dad, and he had a bad slip moving trash to the curb and is now thinking of moving into an retirement village. I've always imagined you guys living here forever, and I wanted to check if that's what you guys want to do too, and if there are any renovations you'd be interested in to make it more comfortable.'