You could use an XSLT transformation.
XSLT stands for eXtensible Stylesheet Language Transform. Basically, an .xslt file allows you to take XML (or any other structured markup language like HTML) and apply a transformation. You could take the XML that Wordpress generates and use it to transform into the XML structure that RSS feeds use (RSS is just XML in a specific format).
You apply an XSLT file against an XML file, and the output is an XML file in the new format. Browsers are capable of applying an XSLT file against the source of a file to create a new version. You could try having one page for the normal XML, and another page that emits a tag that applies the XSLT file, making it an RSS feed.
The downside to this is having to do some learning about XSLT, which can be a bit of a pain and is not used very often. Certain mobile browsers might not support it. The advantage is that it was designed to transform XML and runs very fast.
You might also be able to get Wordpress to do the work on the server-side, making the browser used a moot point.