Chris, thanks for your reply.
I ran the script on the post you linked and found that my index page had an extra line after the last closing php tag. I also looked at the remaining files manually, in case the script missed any (which it did, about 6 files), and I made the changes to remove the extra lines in those files. Those changes don’t seem to have effected my rss-feed output, unfortunately. The empty lines that you pointed out are still there.
Do you have any other suggestions? Is there anything you can tell me about how / where wordpress sets up the RSS feed?