I am asking this question here because it is my understanding that this is the official GAE support site.
The background: I had a website, mysite.com, hosted on somehostingsite.net. Recently, I ported the website to GAE, mysite.appspot.com. This occurred just as the renewal fee from somehostingsite.net was coming due, so I cancelled the somehostingsite.net account. I haven't transferred my domain to another registrar.
The problem: I want to set up my domain with Google Apps so that I can have a url like myapp.mysite.com. So, the verification process to verify my ownership of the domain name presupposes mysite is currently up and running. Mine isn't right now. However, my domain title is listed at OpenSRS but they do not provide DNS support.
The main issue: mysite.appspot.com is free, which is why I ported the website to it.
What is the best way to proceed to get my domain set up with GAE given my current circumstance?
"So, the verification process to verify my ownership of the domain name presupposes mysite is currently up and running."
Not quite: all you need is DNS for your domain up and running, and then you can create a DNS TXT record to verify your domain. See: http://support.google.com/a/bin/answer.py?hl=en&answer=60216
So it sounds to me like you need to get (configurable) DNS hosting set up somewhere. You're going to need that anyway because you need to set up a CNAME record in order to serve you App Engine App off of your domain.