Mail in Mavericks is a disaster for me. Mail opens VERY slowly and cannot be deleted. I can move copies of messages to On My Mac but the original stays in the In Box. Scrolling works then it doesn't then it does. I tried every advice here; nothing helps.

Question

I've read and tried all the solutions proffered to others about Mail in Mavericks and scrolling issues as well.  They either are not applicable (hard drive seems fine; is less than half full; permissions have been repaired; Disk Utility finds no hard drive issues) or don't work (rebuilding, removing envelope files and re-importing, removing various preference files).
I have about 200,000 emails in four In Boxes.  Prior to Mavericks this was not a problem.  I have tried to remove them in case that helps but when I move them to a new folder in "On My Mac" the new folder is (very slowly) created but the original messages stay in the In Box as well.  I went through one box and deleted over 52,000 messages -- or so I thought.  When I closed mail later, I got a message saying the messages could not be moved to trash.  They are in the In Box now.
Maybe the problem is not Mavericks, but it started when I upgraded, and except for scrolling, which has been problematic elsewhere as well but no where more than in Mail, everything but Mail seems to be working ok.
Are other people having problems to this extent?  I can wait a little while for a fix but I get over 2,000 emails a day (yes, a lot of spam) and I don't think I can go on in perpetuity without the ability to delete messages.  I've used Apple Mail since its inception and would prefer to keep it but may be forced out.

Answer 1

Please read this whole message before doing anything.
This procedure is a test, not a solution. Don’t be disappointed when you find that nothing has changed after you complete it.
Step 1
The purpose of this step is to determine whether the problem is localized to your user account.
Enable guest logins* and log in as Guest. Don't use the Safari-only “Guest User” login created by “Find My Mac.”
While logged in as Guest, you won’t have access to any of your personal files or settings. Applications will behave as if you were running them for the first time. Don’t be alarmed by this; it’s normal. If you need any passwords or other personal data in order to complete the test, memorize, print, or write them down before you begin.
While logged in as Guest, launch Mail and set up one of your IMAP accounts. Same problem?
After testing, log out of the guest account and, in your own account, disable it if you wish. Any files you created in the guest account will be deleted automatically when you log out of it.
*Note: If you’ve activated “Find My Mac” or FileVault, then you can’t enable the Guest account. The “Guest User” login created by “Find My Mac” is not the same. Create a new account in which to test, and delete it, including its home folder, after testing.
Step 2
The purpose of this step is to determine whether the problem is caused by third-party system modifications that load automatically at startup or login, by a peripheral device, by a font conflict, or by corruption of the file system or of certain system caches.
Disconnect all wired peripherals except those needed for the test, and remove all aftermarket expansion cards, if applicable. Start up in safe mode and log in to the account with the problem. You must hold down the shift key twice: once when you boot, and again when you log in.
Note: If FileVault is enabled, or if a firmware password is set, or if the boot volume is a software RAID, you can’t do this. Ask for further instructions.
Safe mode is much slower to boot and run than normal, with limited graphics performance, and some things won’t work at all, including sound output and Wi-Fi on certain models. The next normal boot may also be somewhat slow.
The login screen appears even if you usually log in automatically. You must know your login password in order to log in. If you’ve forgotten the password, you will need to reset it before you begin.
Test while in safe mode. Same problem?
After testing, reboot as usual (i.e., not in safe mode) and verify that you still have the problem. Post the results of steps 1 and 2.