Thanks to the work of /u/toasties, one of Reddit's friendly admins, Modmail is now fixed. It's back to working the way it did before. Yay!
The admins get so much crap from some users, that I feel it is important to take a minute to publicly acknowledge the positive changes. Having an access issue fixed within a week on a major website is probably some kind of record. Especially when you consider the fact that I never actually filed an official bug report, instead just whining about it here and on beta. So the admins are obviously listening. And I really appreciate it.