Views does almost what it should. There doesn't seem to be support for nesting lists, which I was looking for. It refuses to create a nested list (below). JQuery and AJAX could've done a great job of theming that into an accordian menu.
Instead, I need to choose between a MM/YYYY view:
Or a page with just years:
That links to months:
None of those are quite what I wanted. Contextual filters were perfect, but don't work on the front page. A taxonomy that contains publish date looks impossible. I would up using a module that creates tabs to manually display the posts for months of that year.
It's a very dirty solution, though. I need to manually create a tab for each year. I'll see if I can do better.
Edit: Whelp. I'm really tired of messing around with that. I themed the Quicktabs block a bit, which is all right. I also created an Archive view with the URL path I wanted: nitkin.net/archives/2012/6 shows all posts from June 2012, and nitkin.net/archives/2012 does exactly what it should. Go with what you can.