I've googled around but can't find any HTML minification scripts.
It occurred to me that maybe there is nothing more to HTML minification than removing all unneeded whitespace.
Am I missing something or has my Google Fu been lost?
You have to be careful when removing stuff from HTML as it's a fragile language. Depending on how your pages are coded some of that whitespace might be more significant; also if you have CSS styles such as white-space: pre then you may need to keep the whitespace. Plus there are numerous browser bugs, etc, and basically every character in an HTML file might be there to satisfy some requirement or appease some browser.
In my opinion your best bet is to design the pages well with CSS techniques (I was recently able to take an important page on the site I work for and reduce it's size by 50% just by recoding it using CSS instead of tables and nested style="..." attributes). Then, use GZip to reduce the size of your pages for browsers that understand gzip. This will save bandwidth while preserving the structure of the html.