My advice for full gamepad controls:
* Have just one button for menus, going directly to quests. From that button, Left shift and Right shift take you to all other full-screen menus (relations, journal, shipyard etc).
* The trickiest part is how to handle inventory given the realtime nature (inspection times, installation times). From a gamepad perspective, the ideal setup is pausing when the inventory is brought up (by default, together with the character screen). This allows you to avoid all control issues: slots can be selected with the d-pad or the left stick, and items can easily be moved around or used.
This is a problem with regard to the timers though, since they can't run when you're paused. One thing you can do is queue up timers (for installation and inspection) so they only start running when you leave the paused inventory screen.
Another option is to finally abolish the inspection times, and only leave the installation times once the inventory is closed.