That's funny, because when I researched it, I kept finding the tahkli!
It's worked fairly well for me.
It's small and portable--in the past, I took it to kids' orchestra performances (sat in the back near the emergency-exit lights) and to board game nights (helps me be patient when the other players think forever about their turns.)
I bought some cotton fiber that was all combed out into a long strip, and that works OK.
Like you, I tried growing cotton. I've been able to spin my cotton right off the seed, without having to pull it off and comb it first. Personally, I like that better than the combed-out long strip I bought, but I don't know if it requires a special kind of cotton or something. I got several kinds: white and brown and green. Some seeds look naked when I'm done spinning, while others are covered with short fuzz, but so far they have all worked OK for me.
I think I mostly spin park-and-draft style, although I slip back and forth between that and drafting while the spindle spins. I think it depends on how much I'm fumbling at a given time
If I focus on how much yarn I produce, spinning cotton drives me crazy. But if I just enjoy spinning it, the amount gradually adds up.
I have daydreams of eventually knitting a short-sleeved sweater in several colors of natural cotton. So far, I have spun "lots" of cotton yarn-- but I don't think it's enough for even one sleeve. So I'm not sure my sweater will ever really happen.