gyozadude

The references for limits of derailleur movement are indeed the small cog and the big cog. But the reference for proper indexed gear and cable tension are the 2nd to smallest cog and larger. Try to avoid using the smallest cog (Highest gear) as the cable tension reference. The fact that you can twist the adjuster barrel(s) on cable tension to cause the chain to move from 2nd smallest cog to smallest means you've probably got too much adjuster barrel unscrewed.

Try this:
a) shifter to tallest rear gear (i.e. the smallest cog outermost).
b) adjuster barrels almost in all the way, except for 1 or 2 turns backed out
c) set H-limit adjustment
d) tighten the RD cable now with some tension (like using one hand to pull on end of cable)
e) try to shift to 2nd smallest cog, and adjust tension until centered on 2nd smallest cog
f) shift through other gears
g) set the L-limit screw.

That should do it. The key is to shift to 2nd smallest cog with first click on the rear shifter and then center using cable tension on the 2nd gear. We shouldn't use the 1st smallest cog as the cable tension reference because various manufacturers often assume zero or minimal tension and no cable housing compression yet and the RD is resting against the H-limit screw. So they usually increase the amount of cable slack picked up by the shifter on the very first click because they try to accomodate all that cable housing compression, pre-stretch in brake cables, etc. So for indexing to work, the amount of slack picked up by the shifter on subsequent gear shifts is consistent and smaller. Hope that works for you.