Forwarding to www, DNS, and Google App Engine

I have a site I'm setting up on Google App Engine. App Engine will let me do that for a subdomain, but not for a whole domain. So I can use www.mydomain.com, but not mydomain.com, for my App Engine site. Google suggests forwarding mydomain.com to www.mydomain.com, which sounds good to me.

So,
1. I want mydomain.com to redirect to www.mydomain.com, and
2. I want www.mydomain.com to refer to Google App Engine.

#1 is doable if my domain is Fully Hosted, since there's a radio button for that. But #2 is not doable because I can't add a CNAME record to redirect www to Google. This is because www already has a DNS record that is locked down by the Full Hosting option.

#2 is doable if my domain is Google Hosted, because www is not locked down in DNS and I can add the CNAME record just fine. But I don't see any way to accomplish #1.

Any ideas? I don't want to go find another host, because I've generally had a great experience here.

Perhaps a new subdomian would make more sense?

* app.mydomain.com - points to Google App Engine
* (www.)mydomain.com - redirects to app.mydomain.com

This way whether the user hits www.mydomain or mydomain they will end up at app.mydomain.com.

You can also mask the address so the user thinks they are at mydomiain.com, though IMO that is not necessary. Users don't care what the url is, so long as the app works.

"To be pleased with one;s limits is a wretched state."
-Johann Wolfgang von Goethe