I apologise for coming off this way. I didn’t intend to look down on you; I wanted to write my post as a detailed tutorial, primarily because this is a recurring issue (I’ve encountered something similar at least once before), and I’d like to be able to link to it if something similar occurs. I have now edited my post a bit to reflect on this.
You are not required to have your domain constantly point to our nameservers. As I wanted to say in my original post, simply pointing it to the nameservers once to be able to add it to your account here should suffice. After the domain is added to an account, you can revert to using the default nameservers, and just add an A record in GoDaddy’s DNS management that points to your website’s IP address.