Well I have been putting it off for too long now, but I have finally gotten around to upgrading my blog. I decided to install a completely fresh version of BlogEngine side by side with the existing version in a new folder. I then used the Blog Importer application found on the BlogEngine Settings page (make sure you are using Internet Explorer for this step) to export and reimport my posts using BlogML format into the new blog. You will want to export your posts from the Settings page on your old blog to somewhere you can easily find, like your desktop. It generates a single XML file and works fairly quickly. You will then need to download the images and files that are linked to your posts using FTP - you'll need the AppData/Files folder (again, I just put this entire folder on my desktop).
Once this was done and I was sure I manually duplicated the few remaining fields in the Settings panel, I simply archived my old blog to a zip file and deleted the entire folder. I then renamed the new folder to match the name of the old one. I noticed that the new install added the dates to the URL by default, but this is easily turned off in Settings if you were not doing this on your old blog. Remember, you want to try and maintain as many of the links as possible to avoid broken links from referring sites. Another gotcha is that it seems that the Blog Importer didn't catch small changes in the slugs - so it doesn't hurt to do a rough side by side comparison if you create your slugs manually or if you typically modify them.
I will keep an eye out over the next couple of days and try and fix any stray links I might have missed on the first pass, but so far I am excited at how smoothly everything went. I will be slapping a fresh theme on this puppy soon, so keep an eye out and let me know what you think!