Rewriting URLs from https:// to http:// in IIS7

I'm trying to rewrite urls from the form:

https://example.com/about

to the form

http://example.com/about

using IIS7 URL rewriting:

<!-- http:// to https:// rule -->
<rule name="ForceHttpsBilling" stopProcessing="true">
  <match url="(.*)billing/(.*)" ignoreCase="true" />
  <conditions>
    <add input="{HTTPS}" pattern="off" ignoreCase="false" />
  </conditions>
  <action type="Redirect" redirectType="Found" url="https://{HTTP_HOST}{REQUEST_URI}" />
</rule>

<!-- https:// to http:// rule -->    
<rule name="ForceNonHttps" stopProcessing="true">
  <match url="(.*)billing/(.*)" ignoreCase="true" negate="true" />
  <conditions>
      <add input="{SERVER_PORT}" pattern="^443$" />
  </conditions>
  <action type="Redirect" redirectType="Found" url="http://{HTTP_HOST}{REQUEST_URI}" />
</rule>

I'm at a loss; I've been browsing the web for examples and trying every syntax I can think of. The rewrite rules I specify simply don't appear to work at all for any https requests, as if all the https:// requests are flat out invisible to the rewrite engine.

rules work fine; see answer below.