Publish to two blogs selectively

I have been searching for months and have yet to find the solution to my problem. I hope I can get some pointers here.

I am currently blogging (or better call recording stuff – I started with that intention) in my private blog. However, as I add/record more stuff in it, I feel there are things that can benefit others if being shared publicly (e.g. technical, traveling hits). I personally have benefited from the generous content sharing on the web. Also, it is easier to share stuff from a public blog (e.g. travel logs, interesting articles). I would like to do the following:

1. Continue to blog everything in my private blog, where it will serve THE place I go to record/find my stuff. Call blog A.
2. At the meantime, set up another public blog with different url. Call blog B.
3. When I publish an article (e.g. post, page) in blog A, the article (including related media) gets ‘selectively’ (and automatically) published to blog B depending on its category. E.g. I create a unique Category called Public, and all posts/pages in Public get published to both blog A and B (with same tagging, categories, medias, etc).

Note blog A and B are eventually independent entity and all reference urls (e.g. media, cross reference to other posts) are different (e.g. blogA.com/** and blogB.com/**). They are separate installations of WordPress ideally. The two sites can have different looks, different menus, which I will manually set up.

I have looked at Multisite, but it doesn’t seem to do #3. Doing export/import is laborious and dealing with two different reference urls can be messy (e.g. medias, post cross reference). The closest I found is to use third party writer (e.g. Windows Live) and once I completed an article in it I publish it to two blogs (one after another). However, WLW (as well as other third party writers) does not work with plugins I am using (e.g. syntax highlighter, upload to folders based on post slug, etc). I am writing from TinyMCE in WordPress.

Has anyone done similar thing I want to do? How do you do it? Any pointers will be much appreciated.