OPTION 1: You could set the URLs of your existing posts on the new WordPress blog to point to the locations on the old WordPress blog, using the linked list plugin. This modifies the permalinks used in the updated feed so that they match those in the old feed; iTunes shouldn't see them as new items.
You could set the FeedBurner feed to use a filtered version of the new WordPress feed that displays only new posts. Here's how:
On the new WordPress blog:
Create a category called 'old' (or similar).
Note the category ID, which can be obtained by browsing to Posts > Categories, then clicking the category you created, and looking for
&tag_ID=4 in your browser's address bar.
Set all of your old posts to use the 'old' category.
In the FeedBurner admin area:
http://yournewURL.com/?cat=-99&feed=rss2 as the 'Original Feed' address. Replace the
99 with the category ID you noted in step two above, and be sure to include the minus sign before it. This creates a feed that excludes all posts in the 'old' category.
iTunes should now see only new episodes that you publish, not older ones. One caveat is that new subscribers won't see anything at all until you next publish something. It's up to you to decide if this is better or worse than old subscribers having to redownload episodes they've already listened to. (I'd suggest that it's slightly better if you have a lot of subscribers, especially if you consider that the feed will soon fill up after you've published a few new episodes.)