I'm actually using Google, but as a POP3. I don't spent $5/month/email address either, I have unlimited ones that I stick into a free one. I have a few domains as well. The Enterprise Google doesn't allow me to check/send POP3 from other services. I have cPanel on the back end, and setup email addresses and forwarding and aliases. I enjoy Google also, chats and I literally live off of Drive.

I have a dedicated IP address - the issue is that Cloudmark is blocking the PTR record at the shared server, which I can only get modified if I have a dedicated server.

So yes, GoDaddy is blocking namecheap.