Over the last 4 years I have been searching for a n autopost solution from one of my own websites to some of my other websites.
The reason why the RSS based method does not work so well for me is that does not import images properly. The best method I have come up with is a plugin that works WITHOUT multisite that logs into a wordpress website through an administrative user and re-post posts based on filters/categories/tags onto other sites by logging into them.
I had a custom plugin like this built once however it kept breaking as wordpress updates were installed.
Pulling posts via RSS works fine from remote sites that you do not have access to, such as news publishers, you then edit and publish these posts on your main site. The plugin I am referring to would then take the post perfectly to other sites based on filters automatically.
This is without a doubt the best method of running multiple news aggregators that consist of websites that cater for different topics, for example you publish posts on the main site under your sports category and the plugin will autopost these perfectly on a sports website you own as well.