Problem (mostly) sorted, was misunderstanding and misuse of style attribute
With Mobi_Unpack v0.54 I do get clean output of your original HTML, which is as you describe. With 'style="text-decoration: none"' as an attribute to the <a> tag the underlining is suppressed on the Kindle Touch. My problem here was simply incorrect use of the style attribute within the tag.
It still does not work for me when done as a CSS style, putting "text-decoration: none;" into a style that otherwise does work for links, but that might just again be a usage problem - I can investigate further now I know what does work.
It would be nice to have a solution that works on all Kindles, but at the moment that does not seem to be possible.
Thanks a lot for your (and other people's) help here - this issue has been driving me nuts!