If the problem is that no one will post in an open thread near the end of it's lifetime, a silly solution would be to automatically create an open thread every day with 10% probability. Now someone considering posting has no reason to wait for a future day to post because the expected lifetime of a thread is always constant, and is ~10 days.
Better would be to have a single thread "Open Thread" where posts older than N days would be moved to an automatically created "Open Thread Date-Date" post.
An even easier fix would be to remove the end date from open thread titles. When someone feels like posting a new one they just do that. This is a sloppy implementation of the first solution.
How about overlapping thread lifespans? This way when a new thread is created, recent comments on the previous thread won't go unread, and discussion can still happen there. A thread on Monday that lasts a week and a thread on Thursday does too, for example, with both threads pinned to the top and included under the Latest Open Thread feed on the side. I suspect this would be easier to implement than your second option. It's more difficult to implement than your first and third options, though.
I've noticed a kind of "LW content inflation" over the years where what was once appropriate for Main becomes appropriate for Discussion and what was once appropriate for Discussion becomes appropriate for Open Thread. I don't know if this is a good thing or not. It seems like if you are asking a question that has an unambiguous answer then you should clearly post in Open Thread because it's fairly wasteful for additional people to see your question after it's already been answered; beyond that I'm not sure.
I fear the thread will wither and die before Friday.
What do you mean? People seem to post in the last days of the 'week' with a reasonable frequency, however, I fear that making the OT a daily thing will just result in more Discussion clutter, less visibility of other threads and less visibility of comments in the OTs.
I share some of your concerns about Discussion clutter and fragmentation the open threads, and think we will understand the tradeoffs better if we have a prototype in front of us.
I fear the thread will wither and die before Friday.
What do you mean?
The previous open thread had 330 comments in its lifetime. The latest open thread had 156 comments on its first day. By 'withering', I mean an open thread half spent on its first day.
As a subjective indication I got the feeling that the quality postings somewhat reduced recently.
Could it be that more frequent open threads discourage from self-contained postings?
That would imply that "comments inevitably expand to fill the available room" because this effect is increased.
I don't think the proposal is a good idea: it adds a trivial inconvenience to posting, and adds more noise to discussion making it harder to find the latest actually open thread. I predict the result would be at least one of: people post in the wrong section, people ignore a number of the categories, or people post less overall.
I'm in favour of more frequent open thread posts, but I think they should remain a single open thread. (Actually if I were making changes I'd probably fold the media recommendation posts into the open threads).
This week's open thread is less than a day old, and has already accumulated more comments than the 15 latest non-open-thread posts combined. I fear the thread will wither and die before Friday.
Going from monthly to weekly open threads was a big hit. Should we ratchet up open thread frequency even more? Should we add more outlets for comments, or will comments inevitably expand to fill the available room?
Proposal for discussion: We follow a regimen of weekly blather threads for the next two weeks, then reassess.
Addendum
I posted a Links on Friday and a Stupid Questions on Monday. In the 5 post-days that they've been up, they've accumulated 32 comments. Based on these numbers, it seems unlikely that these topical open threads will relieve pressure on the main Open Thread and so I've stopped the experiment.