I'm generally able to run my cotton completely dry, thanks to a simple "first burn" technique. I still prefer cotton in my Hadaly (open to rayon tips for that atty, as an aside).
I'm not sure if this is well established or not, but I have never seen it mentioned: the first time install a fresh wick, do the following:
1) Soak the coil section only and then GENTLY cook dry at low wattage
2) Drip onto the coil very slowly until the tails saturate
3) Cook that mother dry. Don't vape it, just run it at your intended wattage until the cotton runs clean. If you're doing it right it will seem impossible that you aren't burning the wick. DO NOT go nuts, coils should stay at vape-appropriate temps.
By this point your cotton should be almost entirely dry, unburnt, and the magic part: your tails should look totally different. Kind of spongy and wispier. Now when you drip/squonk the tails will just devour your juice and will feed your coil much more readily.
I'm not sure why this is so effective, and I am assuming what's actually important here is simply ensuring the first saturation gets immediately vaped dry (so vape that juice if you like), but assuming I've wicked correctly for my coil, I'll vape that thing well past the point where it seems like I'd get anything from it.
I hope this wasn't too confusing. It's such a simple but critical step, and I always do it.