Have you tried pulsing your calf in time with the walk you want to achieve? I'm still very tired, so it makes more sense in my head than I can find words to explain.
I do this, somewhat... a trainer once told me to push the barrel back and forth underneath me with my calves, and my horse has learned very quickly that this is a request for more "umph" at the walk. When we're practicing, if I also start counting out loud with his footfalls "one two three four" he picks up immediately and gets the idea.
I've found that after working "in frame" for a while, my horse loves to be rewarded by trotting out on a loose rein. He gets to stretch over his topline and it feels so gooooood!
Perhaps if you start using stretching down as a reward after work you can both get used to moving out on a loose rein?