By bringing an article to the front page, either with the old comment thread or with a fresh one (plus a reference to the old one), it becomes something that the community is doing.
The main problem with your proposal is that it unnecessarily forces everyone who reads the front page to participate in your project. (Eliezer wrote over 600 posts on Overcoming Bias. If they were all reposted, that would drastically change the character of the front page.)
If on the other hand, the reposts were to appear at a URL that is not currently being used, /r/sequences/ say, then each person could decide whether to participate in your project or to continue to use LW the way they are using it now.
Parenthetically, if I were to write software to support your project, I would create an RSS feed of (new) comments on the (old) posts in the sequences. That way, someone who is reading a post in the sequences knows that if they make a comment (e.g., to ask a question), it will probably be noticed. In fact, the probability that it will be noticed is high even now, but would rise if there were a way for readers to watch for the comment without needing to scan the firehose that is http://lesswrong.com/comments/.
Note that such an RSS feed could be created without modification of the software behind lesswrong.com (since the necessary information is already in http://lesswrong.com/comments/.rss and the new RSS feed can be published at a domain other than lesswrong.com) which is probably a good thing given the difficulty some here have had recently in getting the attention of a someone with the authority to pull changes into the software behind lesswrong.com.
Given that
1. Deciding to read and actually reading the sequences is 'work'
2. Reading the latest frontpaged article on LessWrong is 'fun'
3. We frequently have gaps in the posting rate of articles that make it to the front page
4. There are many people who joined this community after the sequences were written and haven't gone through all of them
...would it make sense to start bringing articles from the sequences to the front page, either at a set pace or whenever there is a gap in posting?
I have actually read most of the sequences, but wouldn't mind going through them once again. However, taking it up as a project seems like too much work. By bringing an article to the front page, either with the old comment thread or with a fresh one (plus a reference to the old one), it becomes something that the community is doing. Following things that a group you belong to is doing is fun. But for that to happen, we need to share a common pointer to which article is 'the one we are reading now'. Hence, the front page.
In short, I think if people in this community reading (and re-reading) more of the sequences is something we want, then recycling them through the front page is also a good idea.
If the barrier is implementation modifications needed, I may be able to assist.