Indigohat, thanks for the suggestion. I messed around with the permalink settings and .htaccess file and discovered the problem.
My .htaccess file was just in the wrong directory. I have WordPress installed to /wp but my blog index appears in the root. I copied .htaccess to / and left my archive format as /archives/%year%/%monthnum%/%day%/%post_id% and now the comments and submit form work properly.
I had been unsure of which directory .htaccess needed to be in, but I thought it was /wp since it needed to be there for the template editor in the control panel to access it. It just didn't occur to me that after changes, I needed to copy it to root just as I did with index.php. To save me a little trouble, my husband set up some symlinks for me, so I can skip copying those files from /wp to / .
In summary, your .htaccess file needs to be in the same directory that you list for your blog homepage.