I have a T Flight, bought it with Beta over a year ago. (Sorry to feed the necro here)
I use the hat ("mushroom") for power distribution. This is essential, in my opinion. The better HOTAS units have two hats where you could use the second for thrusters but power distribution is more important and thrusters can be mapped to others. But I also have the "3" button mapped as my Shift key so while holding that down I get double the functions 3+hat left/right does head look left and right
Lateral thrusters are the rocker axis on the throttle, verticals are the two buttons next to the rocker. But Shift + Thrust Up engages supercruise and Shift + down thrust engages hyperdrive.
Boost is "8" so you need to stretch your left thumb down - it's the hardest to press accidentally. Shift+boost opens hardpoints. I group the shifted functions to make sense (at least to me!)
the only two that don't have a shifted function is the triggers. I can deploy scoop, gear, target switching (admittedly this is the one place I could use more flexibility as I'm always toggling through targets)
Using this method I can do almost everything from the sticks including request docking and all Starport Services, etc.
oh and under the Landing Override I have the hat setup for lateral and forward/reverse thrusters to assist in docking just as you mentioned.
I'm also a leftie who does almost nothing with my right hand. The way I've segmented the controls fits that very well, as my left hand does more walking around the throttle while my right is spent mostly driving the ship