--Locked out of iCloud account on Mac
So one day when I went to unlock my MacBook from sleep mode, it asked for my password (as it should), my Mac OS X account is linked to my iCloud account and doesn't have a separate password, so I enter my iCloud password, and normally it accepts it, not this time however, the login window just shakes and doesn't let me in, so I go and reset my iCloud password, I enter the new password into my MacBook, still won't let me in, even though my other devices have no issue with it, I reboot the computer, thinking that it just hasn't updated yet, unlock the FileVault encrypted drive, and since I forcibly rebooted it, it goes past the main login window and just lets me in without a password, I try to update my iCloud password via the iCloud preferences, it accepts it at first but keeps saying I need to verify it, I verify the password multiple times, does the same thing, I reboot it again, then try to act like I forgot my FileVault password, and reset it when the drive unlock screen comes, thinking that resetting the password this way will make the Mac realize there's a new password, evidently this wasn't the case, because I still can't get past the login screen with either the original password or the two new passwords I set via resetting.
I tried resetting the account password via the recovery mode, but obviously iCloud passwords take precedence over local account passwords, so it changes nothing.
Is there anything I can do to regain access to my Mac short of reinstalling OS X? And if I do have to reinstall OS X, will my personal data remain intact, if not, can I backup my stuff before reinstalling without having access to my account?
MacBook Pro with Retina display, OS X El Capitan (10.11.1)