The idea here is to have a site (any site) which somehow has the user’s WordPress user-name and login (maybe as part of a sister site) to allow him to write a post on his own blog. The idea I have now is basically a simple form sent (perhaps with curl or socket) to the user’s blog admin_ajax.php, even though it is strictly not an AJAX call.
Are there any other methods which I could try or is there something built into WordPress itself already?
WordPress supports XML-RPC protocol for such things. That is how desktop blogging clients work.
Alternatively you can try to set it up via post by email.
You can enable guest posting, and give then username and password for guest account. It is security efficient way. Also you can keep an eye before post publishing.