I have never found a way for a screen reader user to do "direct jumps" to new material with a screen reader. Screen readers don't seem to differentiate in any meaningful way between quoted and fresh material, and give screen reader users a way to jump between chunks of that fresh material when they wish to do so.
Am I missing something? Is there already a way this can be done with ease? If there is, I don't know what it is and I have plenty of evidence that most screen reader users don't, either, even those who've been using them for a very, very long time.
I use Thunderbird, and it turns quotes into block quotes. I can hit , to skip to the end of them. There used to be a setting to turn it off and leave the >, but it doesn't seem to work anymore.