I must add Adrien from Acymailing recently wrote he could integrate quite quickly seblod lists as Acymailing tags for his automatic newsletters. I'm note sure it will include the user's criteria. I guess it will only be seblod lists and there won't be a way to have customized lists according to the user's profile.
I'm sure Adrien from Acymailing can include seblod tags so that the newsletter can take seblod lists. He also confirms he would allow the end user to specify his own sending process frequency (day, week,...) but it would take more time to build this feature.
According to me the real issue would be then to be able to let the end user specify his own query. The objective is not to receive the latest contents from admin defined categories (or example) but to let the end user specify his own criteria so that the seblod search would take this user's profile values and reinject them (live value - button 2) so that he would receive his OWN query.