The BlockCMS editor had everything except for the section that let you pick which pages to display in the block...
What I saw when I opened the developer console explained everything. The browser was blocking non-SSL content that the BlockCMS module was requesting. The blockcms.js JavaScript file was the one being blocked and that file is responsible for providing functions that populate the BlockCMS editor.
After some digging around I found the problem. It was in the modules/blockcms/blockcms.php file.
The _displayAddForm() function was hard-coded to use PS_BASE_URL when adding JavaScript files to a page. It should have detected whether SSL was enabled and used an appropriate base URL instead. Since I knew that I wasn't going to switch SSL off, I replaced that with PS_BASE_URL_SSL and saved the file (this is just a quick fix, I didn't want to spend time on the correct fix that detected SSL settings).
After making that change and refreshing the BlockCMS editor, all of the CMS pages were now visible and I could again select what was shown and what wasn't!
-i