This is a really weird exception, sorry. You've kind of learned these reading, but they're like... weird variations of them.
Take the さ from 早速, the おつ becomes おと, and then the 女 kun'yomi め (hey that one's normal!). And you get さおとめ. You might need to just memorize this one.
Long ago, women who planted rice seedlings were called Saotome or Ueme.
In Saotome Katsumoto's children's literature there are many works with peace as their theme.
Apparently, when she made her debut, actress Saotome Ai played the lead character of the same name in the film adaptation of the manga "Ai to Makoto," then just adopted it as her stage name.