What's the best way to represent a stage script in HTML?

More proper (semantically) and shorter would be to use definition lists:

dl {
  overflow: hidden;
}

dl dt {
  float: left;
  width: 30%;
}

dl dd {
  float: left;
  width: 70%;
}

<dl>
  <dt>Jeff</dt>
  <dd>This sure is a nice website we've got now.</dd>
  <dt>Joel</dt>
  <dd>It certainly is. By the way, working at FogCreek rocks.</dd>
  <dt>Jeff</dt>
  <dd>Of course it does. Have you played Rock Band yet? It's a lot of fun.</dd>
</dl>

I'd say

<dialog>
  <dt>Jeff
  <dd>This sure is a nice website we've got now.
  <dt>Joel
  <dd>It certainly is. By the way, working at FogCreek rocks.
  <dt>Jeff
  <dd>Of course it does. Have you played Rock Band yet? It's a lot of fun.
</dialog>

as defined in HTML5.

Of course, you'll need a <script>document.createElement('dialog');</script> to get IE to do something sensible and a dialog { display:block; } in your CSS to get it to work completely.

My favourite example of marking up something like this is one of Tantek's XHTML compounds http://tantek.com/presentations/2005/03/elementsofxhtml/ (check out the conversation bit)

In summary it goes like so:

<ol>
  <li><cite>Jeff</cite>
    <blockquote><p>This sure is a nice website we've got now.</p><blockquote>
  </li>
  <li><cite>Joel</cite>
    <blockquote><p>It certainly is. By the way, working at FogCreek rocks.</p></blockquote>
  </li>
  ...etc...
</ol>

Not sure how you'd mark up stage directions etc... Maybe you'll end up creating a new microformat :)

Also that markup has some ideal CSS hooks, with discrete LInes unlike a definition list.