I did it! No more Feedburner!
As part of the switch to a self-hosted blog, I decided to minimize the number of third-party services I depend on to make everything work. So after a good deal of fiddling, I have been able to cut the cord that was tying me to Feedburner. WordPress has built-in RSS feeds, both for posts and for comments, and I don’t have any problems with either of them. Even better, I was able to install a plugin that allows readers to subscribe to e-mail updates from a very easy-to-use form that I put right in the sidebar. No more clicking on a link that takes you to an entirely different website to subscribe to e-mail updates. It’s also better to have that subscribe/unsubscribe form in a visible location on every page instead of just having a little link that says "Get the email sitting up near the top of the page next to the archive. Maybe now I'll get some e-mail subscribers 😀 . Either way, I really like this whole layout better than anything I had with third-party services. I only hope my readers enjoy it as much as I do.