I fixed all the pages to have the extension .html instead of .shtml. The .shtml was leftover from when I used to use server-side-includes instead of a combination of Blogger templates & Webby layouts to handle common layout issues. Here's the content of the .htaccess file I used to make sure old links are given a permanent (301) redirect to the new extension:
RewriteEngine On RewriteBase / RewriteRule ^(.*)\.shtml$ /$1.html [R=301,L]
During the process, I noticed that Blogger wasn't producing an archive index page anymore. So I added archives to the sidebar for each blog. I made my css rules a bit more generic by making sidebar sections a class, instead of duplicating rules for different ids.
All of this took a bit longer than it should because any changes on the Blogger side required republishing the whole site (actually twice, once for the main blog, once for the politics blog). Whereas, for the non-blog content, I could run Webby locally, rsync it to my VirtualBox Ubuntu Server VM, and test it locally. So my next task is to figure out how to turn an export of this blog into Webby source files so that I can manage the whole process locally (and get my blog posts into version control as a bonus).