Vlk,
This may have fixed it!
I did log off and back in (quite a few times, actually). The user was not an admin, so I setup an account in Outlook with an administrator account. I noticed something new -- the Avast Outlook splash screen came up in this admin account when opening Outlook. No splash screen on the other User account. No errors in Outlook in the admin account, either... so I tried the regular user account again, and it now has the splash screen, and no more errors!
If anything else comes up, I'll let you know. Thanks!
Btw, the error.log and warning.log files were empty (I had emptied logs previously... when first installing Avast, it found some stuff like the Netsky-Q in some spam emails)