I am still just learning, but I've experienced the same problem you're having. I just did a new build (28g, 5/6 wrap 2mm diameter) and finally got the cotton just right. I read something yesterday about the guy recommending not "twisting" it to get it through the coil. So I kept that in mind while I proceeded to twist it in...
What I did differently was I wasn't so aggressive in twisting it so tight that I could thread it through a needle, I just lightly flattened and pulled and then worked one end to a "point" just narrow enough to get through the coil. I was able to see what RIP Tripper says about being able to work the wick through the coil back and forth with some resistance but not a lot. Once I juiced it up, I actually saw the cotton expand for the first time.
Keeping the cotton light and fluffy and dense enough to feed the liquid up to the coils but not so packed that it gets choked and slows down the process (leading to the dry hits). I just tossed an earlier build with cotton soaked in juice but hitting as dry as the Sahara.