I wonder if you could add a tiny bit of oil or extra LI to the spots where your hat rubs? It might look greasy after you take the hat off tho...
2B/fine to med texture/med porosity

Started CG on 5/5/12!
Battling dry/itchy scalp since April 2010.... Starting to WIN!
Low Poo: Nature's Gate Tea Tree Shampoo
Cowash: GTTTT or GVPCB
RO : Ion Effective Care
LI : KCKT or GVPCB
Stylers : FSG
PT : IAgirl's PT w/ acv, coconut oil, GVPCB, herbs, green tea