i dont have much experience with skimmers, but i would imagine that you will have better success by turning it off. Skimmers in general take out "organic junk" from the water. This "junk" is what should make your tank spike since it will decay and create ammonia.
as far as your media, this is usually where the bactera grow. Since you have lr and ls, its not as important, but should only increase the surface area to provide for your bacteria.
IMO, i would get rid of as much filters and meda as possible and let your rock and sand take care of it. This does mean for less capacity for your tank (ie.. less fish) and a longer cycle, but its my personal preference to use the rock and sand instead of media and filters and i also give plenty of time and let nature take its course.
I do have one mechanical filter on my tank, and i replace it every week. its a thin peice of filter for my w/d which is very inexpensive when bought in large sheets. Other than that, i dont touch the rest of my tank. All my powerheads have their filters removed, the bioballs are only in my W/D to reduce the sound of water dripping, but i had removed them for a good month with no spikes (i took a little out each day)
So, basically two points.
turn off skimmer
give plenty of time for the cycle.