What does this mean, as a programme slogan?
It does not mean slacking.
In Step Eleven (page 86), 'take it easy' is specifically in the context of asking God for input. We do not ask in a panicked, impatient, or imperious way. We ask simply and calmly, then wait and listen.
'Easy does it' is presented as a slogan on page 135.
Based on the preceding material, I take this to mean: don't force change. In other words, we take the action concertedly, but internal and external changes take place when they take place. By extension, we do not force change on others, either.