I would go through the CSS and delete each useless line there. Anything that is only adding a font, or repetitively setting the line-height, margins, default font-size, etc. can probably be deleted.
Once you have cleaned up the CSS, calibre's CSS cleanup tool (but not Sigil's, IIRC) will delete both unused CSS style rules,
and do-nothing CSS styles in the text. Use this, and you will end up with just a bunch of:
Code:
<p><span>lorem ipsum</span> <span>lorem ipsum</span> <span>lorem ipsum</span> <span>lorem ipsum</span></p>
or something close, depending on how many styles you thought might actually be useful.
The final stage will be to use Diapealer's "Diaps Editing Toolbag" plugin for calibre, which has a tool to delete empty span tags (ones which have no style).