You wont' get a loose back until you get flexiblity and length in the neck
The walk you are looking for is an amble with impulsion (loose and flowing but with energy)
Lengthen the neck by opening the rein on the outside (some connection and a little jiggle help sometimes)
You don't need the inside rein to get bend once you have the neck working for you. Your inside leg and the lengthened neck on the outside will get the bend on the inside.
Switch it up -- counter flexion, flexion, straight, repeat.
If you aren't getting enough impulsion, make sure your legs are open to allow the movement and if that doesn't work then use the whip.
Make sure when he does move forward that you move forward with him.