I think it is fine to do a walk/run routine and to just walk or do a slower pace, as necessary. Doing 100 or 200 meters slightly faster is also beneficial, and it seems that is what you are working on including.
It is perfectly normal to feel sluggish on certain days and there are many factors involved, so do not be discouraged if progress is off your expectations.
It sounds like you are doing fine with the program, and just slowly push out the total miles, even if you are walking briskly most of the time because that will also increase your endurance and comfort levels with greater distances.
Wishing you all the best.