But again, I'm a total noob, my 5D3 is my first DSLR and I'm trying to learn everything it *can* do, and keeping in manual most of the time, is the best way to figure things out IMHO.
I can't say that your approach is wrong, but I don't agree with "keeping in manual most of the time, is the best way to figure things out."
Learning how to use the camera in manual mode will probably help you understand exposure. But, it will do nothing to help you learn some of the other things your camera is capable of. The Av and Tv modes are valid tools and they are worth understanding and using.
This thread has demonstrated a couple times that there are people who are stuck in one mode and think that it's the only "real" way to use the camera. They try another mode like Av once and because they have never spent any time using it before they think it doesn't work.
You need to spend time learning other capabilities of the camera before you rule them out.
Personally, I don't see any reason for manual mode to be the "best" way to learn about exposure. The best way is to understand what the camera is doing (whatever the mode is) and see what the effects are. If I understand what aperture and shutter speed affect, then no matter how they are set I can figure out what's happening with the exposure.
When I shoot in Av or Tv mode, I don't ignore the other value just because I'm not setting it. If I have the shutter speed set to 1/1600 in Tv mode, I do check what the camera is giving me for aperture. If I don't like it, I change the ISO, exposure compensation, or shutter speed. I pay attention to what the camera is telling me and I make the decisions.
If I decide to work in manual mode, it's almost exactly the same thing - except no settings change on their own. I'm still looking at aperture, shutter speed, and ISO - I just don't have exposure compensation in the mix (which isn't needed here if I'm fixing all the others).
Personally, and everyone can be different, it seems like a waste to have a nice camera and never experiment with different modes - even while learning. And after "mastering" one mode, you are allowed to use the others. But if you never try them out and practice with them, I can see that you might think they don't work as well as manual mode.