This is one solution to my question, but it requires routing the feed through an additional server.
1. Use Yahoo pipes to sort your feeds as you like (all you need are the "fetch feed" "sort" and "pipe output" modules), and create a pipe.
2. Install the FeedBurner FeedSmith Plugin for WordPress. This routes your feed through FeedBurner, which is a reasonable option if you also want to use that service, but you can also use this plugin only to redirect your feed to your Yahoo Pipe. The FeedSmith plugin consists of a single php file.
3. In your Dashboard you should now find "Feedburner" under the "Settings" listings. That link gives you a screen entitled "Set Up Your FeedBurner Feed." In item Number 2, paste in the address of your Yahoo pipe. (...pipes.yahoo.com/pipes/pipe.info?_id=[some number])
At least it worked for me. But it really seems you should be able to directly add a function to your WordPress installation that would perform this simple operation, so it isn't necessary to rely on a second server.