After much experimenting, I found three Websites which allowed parsing of the Blogger feeds:
1) www.feedburner.com
2) www.2rss.com – the free version has supporting ads
3) feedsweep
With feedburner I found that it does not seem to be reliable, integrating it into my Javascript code worked only sometimes.
atom2rss was pretty fast and worked well, but added these ads to my blog. The no-ads version costs $14.95.
feedsweep has some advanced customisation, but takes some fiddling to get it blend in, and it does not have all options referred to (e.g. background colour for the blog title).