In terms of what you've written, blocking a page via robots.txt doesn't remove it from the index. It simply prevents the crawlers from reaching the page. So if you block a page via robots.txt, the page remains in the index, Google just can't go back to the page and see if anything has changed. So if you were to block the page via robots.txt, and add a noindex tag to the page, Google won't be able to see the page with the noindex tag to remove it from the index because it's blocked via robots.txt.
If you moved all of your old content to a different folder, and block that folder via robots.txt, Google won't remove those pages from the index. In order to remove them from the index, you would have to go in to Webmaster Tools and use the URL removal tool to remove that new folder from the index - if they see it's blocked via robots.txt, then and only then they'll remove the content from the index - it has to be blocked via robots.txt first in order to remove the whole folder with the URL removal tool.
I'm not sure though if this would work for the future - if you removed a folder from the index, and then added more content that was indexed previously afterwards, I'm not sure what would happen to that new content moved to that folder. Either way, Google will have to come back and recrawl the page to see that it has moved to the new folder, and then remove it from the index. So either way, the content will only be removed once Google recrawls the old content.
So I still think a better way to remove the content from the index is to add the noindex tag to the old pages. To facilitate the search engines reaching these old pages, I'd make sure there is a way the engines can get to them - make sure there is a path they can take to reach them.
Another good idea I saw on a forum post here a while ago would be to create a sitemap containing all of these old pages you have indexed and want removed. Add the noindex tag to the sitemap - using the Webmaster tools sitemap interface, you'll then be able to monitor the progress of deindexation over time - by checking how many pages on the sitemap/s of the old content are originally indexed as reported by webmaster tools, and then you can see later on how many of those pages are still indexed, this will be a good indicator for you of the progress of the deindexation.