Is there a way to force them to update their profile first, then get taken to that simple subscription upgrade/payment area? Without messing up the flow for new subscriptions?
CBSubs doesn't currently have a feature like this. I believe it's planned for a later release, but for now the only way to do it would be to develop a custom CBSubs plugin to add new fields to the basket page.
I suppose you could try using CB Auto Actions to redirect to profile edit of those fields are incomplete, but if you're hiding those fields via CBSubs plan it's basically an infinite loop of never being able to subscribe. So it depends on your configuration.