Hmm.. when I make that change it won't update as some other packages (like mailgun) require "dev".
That's not right. If we're talking about the mailer package, it definitely has stable releases.
What may have happened: since your composer file allowed dev versions, while installing the mailer you may have added a version constraint that doesn't yet exist as a stable release.
If you're worried about unstable versions, setting the constraint on a single package doesn't make the problem go away. Your project and all its dependencies can still install unstable versions. Even if laravel/framework itself is stable, dependency installed by it are not.
I'd switch to stable and fix the conflicting version constraints one by one.