How can I store server-level connection string in applicationHost.config?

Question

I have a connection string that all of the applications on my site need to know about. I know that I can put it in machine.config or root-level web.config but let's say that those options are not available to me and the only thing I can do is to modify applicationHost.cofig.

I have tried this and the connection string does appear in the collection of strings for my app under IIS Manager (with an Entry Type = Inherited). But, when I access it from my application like so:

System.Configuration.ConfigurationManager.ConnectionStrings

it is missing. Here is my applicationHost.config snippet:

<location path="Default Web Site" overrideMode="Allow">
  <connectionStrings>
      <add name="ConnectionString1" connectionString="blah" />
  </connectionStrings>
</location>