The exact functionality you're after can be found by using the Shift Switcher, Ring Switcher or Static Application Switcher functions in CompizConfig Settings Manager (CCSM).
(If you need install instructions for CCSM, let me know in the comments)
Using CCSM enable Shift Switcher under the Window Management section.
You will need to disable your current Alt-Tab keybinding, and rebind Alt-Tab to Initiate Key or Initiate Key (All Workspaces).
Take care using CCSM, while Ubuntu is more stable than in the past, fiddling with the wrong settings can cause crashes.
Shift Switcher also comes with 2 different Shift Modes, Cover and Flip - these modes change the visualization, but the basic functionality remains.
Setting the Initiate Key key bind brings up the switcher, and you can freely navigate between your windows with the left and right keys. To bring the selected window to focus, you must select it with the Enter key. This is different functionality to the other switchers.
All the settings can be altered to change the visual effects of the switcher.
Same as above, Enable Ring Switcher in CCSM, and set the Next Window Key (All Workspaces) key bind to Alt-Tab.
The difference in functionality between this (and the below) switcher, and the Shift Switcher is that to navigate between windows you must hold down the Alt key for these switchers. As soon as you release the Alt key, the switcher focuses to the current window.
You can play with the settings through the tabs for Ring Switcher.
Static Application Switcher
This is the least graphical of the 3 switchers, it is like your old-school Alt-Tab from Windows 95 days. To get it working exactly the way you want you need to set the following key binds:
- Next Window - Alt-Tab
- Prev Window - Shift-Alt-Tab
- Next Panel - Alt-Right
- Prev Panel - Alt-Left
This is another switcher setting under Window Management but I didn't test it as it bugged out for me - so I'm not sure whether this is just the default switcher, or some different one.