iCloud email issues

For the past few weeks I've experienced strange iCloud email issues (only iCloud - not other mail services) across all of my devices. The problem is that it's intermittent and the problem acts differently on each device! (And before you ask, all devices are running the latest versions of the OS.)

• First problem: When I open mail, whether it's on the Mail app on the iMac or iPhone or iPad, the message preview list shows all available messages. However, when I click on a message to read it, I either get a blank message screen or a "Loading" message. A times it can take a minute or more to load. At other times, the message never loads. The weird thing about this is that I can open Mail on a different device (say, the iPhone or iPad) and some of the messages are available even though they aren't on the iMac.
• Second problem: Syncing. Let's say I do have some messages I can read on one of the devices. I'll read them and/or delete them, but on the other devices, they still show up as non-read or in the case of being deleted, they still appear in the inbox instead of the trash. Again, if I wait anywhere from a few minutes to, in some cases, hours, things finally sync and all devices show the messages in their proper states. (Other apps sync fine, such as Notes or Calendar)
• Third problem: Online iCloud.com - I see the same issues here, not only on a Mac (or other Apple device when logging in via Safari), but I see it with other browsers as well, even on PCs! In some cases, when I try to activate the online "Mail" app on iCloud.com, I get an error message saying that the "app can't be loaded". All of the other iCloud.com apps work perfectly.

So, I've done all of the usual stuff:

• "Rebuild" the mailbox (in Mail on the iMac - don't know how to do that on iOS devices.)
• Turned off "syncing" on all devices (eliminating the iCloud account from the Mail app) then reactivating it. Doesn't help.
• Rebooted all devices.
• It's not my home WiFi since this happens on multiple WiFi or cell systems.
• Deleted the "Trash" from my iCloud mail account

To be honest, I think I have a hosed iCloud mail account. I don't know of any way that I can directly "reset" the account on Apple's servers. If this is the case, I guess it's time to call Apple to see if they have a solution. But I thought I'd try the brain trust here first. I've used iCloud email for a long time and I've never had consistent problems with it. It's now to the point where it's becoming unusable.

Any ideas?

John