Switching the feed is simple, and again I've done this at least 3 or more times, recently including one extremely popular music podcast that gets over 1000 downloads a week.
All you do is copy your existing podcast XML/RSS file and giving it a new name. Set that new one up in Feedburner so it is happily running, and checks out ok.
Once you've done that, go back to your original podcast XML/RSS file, and change the contents of the original to the following:
<?xml version="1.0" encoding="UTF-8"?>
<rss xmlns:itunes="http://www.itunes.com/DTDs/Podcast-1.0.dtd" version="2.0">
That will tell iTunes to go to your new feeds location, instead of the original one.
Hope that helps.