Dear Gilbert
Sorry for the delay. Been away.
I'm not sure how to assist you precisely, but have the following suggestions which you may have tried already as you sound very clued up.
Starting with simplest & working up from there:
Disc Utility, click on Mac HD and Repair Permissions.
Sounds like you've done this already? Click to highlight each Mailbox, then from Menu Bar choose Mailbox then Rebuild. If you've already tried this, then next step:-
Because there might be cache or other similar problems, Download OnyX from the Titanium website (Link:
Titanium's Software • Index page).
This is a highly respected and safe product widely recommended on this forum. Make sure you download the version for Mavericks. After download, open in the usual way, enter your admin PW when asked.
You can get Onyx to check out your HD but I would cancel this bit and go straight to the Menu from which choose "Automation". Check all the boxes. This will clear out your caches, rebuild mailboxes and lots more.
At the end of the process, you will need to reboot. OnyX has sorted out many problems for many people. I hope it does for you. Report back.
Ian