Turns out the problem was that I hadn't realized that <Set name="handler">
essentially 'overwrites' my default handlers. So, to fix it, I changed the last few lines to
<!-- add the rewrite handler to the server -->
<Set name="handler">
<New class="org.eclipse.jetty.server.handler.HandlerCollection">
<Set name="handlers">
<Array type="org.eclipse.jetty.server.Handler">
<Item>
<Ref id="Rewrite" />
</Item>
<Item>
<Ref id="oldhandler"/>
</Item>
</Array>
</Set>
</New>
</Set>
where oldhandler
refers to a previously declared <Get id="oldhandler" name="handler"/>