Rayon does shrink when wet/hot which is why it needs to be tighter in the coil than cotton, which expands when wet since it actually absorbs rather than transports the liquid on the surface like rayon does. The expansion of cotton can actually work against its ability to transport liquids, sort of like choking.
I tried cotton and couldn't get past the taste of sucking on a wet t-shirt (or insert clothing article of your own choice). Rayon, when really tightly wicked, will produce what some call a "nutty" flavor. My taste buds haven't tasted that which makes me really surprised at how noticeable the taste of cotton was to me. YMMV.
In terms of purity, you aren't going to get a much more pure form of cellulose than rayon. Yes, many chemicals are used in its' production, but those are washed away in the final product. Given that rayon does not absorb like cotton, transports on the surface instead, there is nothing left internally. If you're truly worried about it containing chemicals there is a medical grade available, Tidi, which is used as an absorbent pad during surgery, for example.
As with wicking using any material, it takes a little time and experimentation to get it right.
I've been there and done that with all the pros and cons of both cotton and rayon. Rayon works for me, you can have my share of all the organic cotton you want.
