It sounds like your walk-cycle action doesn't have "has stride length" ON. That makes A:M try to match the progress thru the cycle to match the progress along a path.
Almost by definition a cycle is something that is repeated exactly over and over.
a "second chor action" would allow you to add keyframes independently of the cycle action to vary the position of bones from where the cycle puts them. I dread meantioning it because it's hard to explain in text here on a forum. Hopefully someone will pop in to do that.
As an aside, i'd just mention that if you really need a walk to vary, animating the steps individually is the way it would normally be done, with no cycle at all.