ICloud reminders (web site) – missing features

Even though the Apple support article referred to doesn't specificaly say this (I'm assuming it's because @icloud.com was only introduced recently and the article was never updated), what goes for @me.com and @mac.com goes for @icloud.com (they're all aliases for the same address).

ie, read: Some Apple IDs, like those ending in @mac.com, @me.com or @icloud.com, can't be changed.

So no, unfortunately you won't be able to change.

iCloud: About your icloud.com, me.com, and mac.com email addresses http://support.apple.com/kb/HT5441

I fixed it! All you have to do is make sure reminder sync is on in Settings->icloud, then open your calendar app, tap calendars at the bottom, and pull the calendars down to refresh. This will refresh your reminders as well. Open the reminders app and all your reminders should be back.

Note, I had also tried all the things in the question before doing this, so I don't know if any of those actions are required beforehand.

Also note, you'll probably get an idea as to whether this will work for you or not if all your calendar settings are scrambled, as mine were. Many of the custom colors I'd set we're changed, as were which calendars were selected to be visible. Other clues are in my comments under the question, such as changes in my icloud settings and the inability to create new reminders & reminder lists.

One other thing I changed that I believe is unrelated, but I figure I should mention for full disclosure is, I changed my default email in the settings app from an icloud address to my me.com address.