The first step is to remove the forward motion of your character from the walk cycle. I realize this may become quite a chore depending on how you accomplished it, but it’s necessary. If the forward motion remains part of the NLA strip sequence it will always reset to the start of the motion, the same way the other parts of the walk cycle do.
It may be possible to retain the forward motion, though, depending on how it was created in the first place. This can be done by duplicating the original walk cycle + forward motion Action and stripping out all keys except those that create the forward motion. But this will only work if the forward motion is pretty much independent of the other motions.
So the goal is to have two Actions, one with the character walking in place, the legs, arms, etc., all moving but no forward motion. The second Action is only the forward motion, and it covers the entire range of the walk, not just a single cycle.
The walk-in-place cycle is made into an NLA strip and duplicated as needed to cover the range of the entire walk, say ten steps worth. Then you have the option to create an NLA strip of the forward motion as well and place it in the Editor to blend with the cyclic motions. Now your character moves forward (powered by the second NLA strip) and also moves its limbs (powered by the multiple copies of the walk cycle strip). The NLA Editor is designed to combine Actions in this way.
I’m pretty sure it’s also possible to just leave the forward motion as an Action to run in conjunction with the repeating NLA strips. But I usually like to keep it all in a common Editor when possible.