Hi Andy,
I'm not aware of any problem using multiple instances of Html content feature on a page with slide show enabled on each of them.
If you're managing to use multiple slide shows in one Html instance using syntax like you posted, you could change it and move the hard code styles also to CSS. While you can't use multiple classes in the setting "CSS Class for Slide Container", you can put multiple classes in your markup to add some different style rules to each div like this:
<div class="slideshow slidehow1">...</div>
<div class="slideshow slideshow2">...</div>
<div class="slideshow slideshow3">...</div>
then in CSS put
.slidehow1 { float: left; width: 250px; clear: left; margin-right: 15px; }
.slideshow2 { float: right; width: 400px; clear: right; margin-left: 15px; }
.slideshow3 { float: left; width: 600px; clear: both; margin-top: 20px; background-color: #eef5fb; }
Hope that helps,
Joe