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And I've just found this:
I don't know how long this service has been going - I certainly wasn't aware of it before - but I've just tried it out on the front page of my site and it works wonderfully. It's exactly what I've been looking for, for about three months.
I have zero affiliation with this service, but I'm so delighted with how it works, you'll have to excuse me my out-of-character evangelising about it.
However, if you're using .asp, sticky me and I can give you the rss/asp code to use--it's really pretty simple, and you can control it through a .xslt file. It works well for me on my .asp pages.
Good point... although given that it would be duplicate content, I'm not sure that I would want it to be indexed. Especially as I may decide put the same RSS feed on several other pages as well.