Hopefully Blogger will be enhanced in the near future to provide this functionality without having to change my feed's URL.Guess what... Google has enabled redirection of Blogger feeds. This means that Blogger will redirect all requests for feeds to a URL you supply in your blog's settings. I have configured it to redirect to FeedBurner (which picks up the original Blogger feed).
I enabled it yesterday and the first numbers are starting to show up. Combined with the logs and statistics provided by Google Analytics, they should give me a pretty good idea of the number of visitors/readers.