BASIC authentication isn't actually all that great. Most of us use form-based authentication most of the time. BASIC authentication is considered less secure and logging out of apps may require shutting down the client app (browser), which isn't something I want to do considering how many tabs I typically have open.
One thing to note is transport security and authentication are 2 different things. You don't actually need any sort of authentication just to get TLS (https).
I can't see anything that rings alarm bells in your samples (hint: use the Code button to format stuff like this). Which is why I waited to see if anyone else did. About the only other thing that I can think of is that you check your server.xml connectors. I got burned a while back because a form-based connector was being used when a basic connector should have been (or maybe the other way around. I forget).
An IDE is no substitute for an Intelligent Developer.