If the cone isn't water soluble (which you could remove with cowashing), baking soda and ACV will not remove it. You can low poo with one that contains Cocamidopropyl Betaine if you don't want to jump straight to a sulfate shampoo. Cocamidopropyl Betaine will remove any and all silicones. If you choose to go with a sulfate shampoo, Suave Naturals are all silicone free (and cheap).
CG since 11/2011
2c /3a F /Mii, low porosity

Winter Products /Routine:
Clarifying: Herbal Essences Tealightfully Clean
Low Poo: Renpure Luxurious Argan Oil
Co-washes: Suave Naturals Tropical Coconut or Daily Clarifying
RO:
Tresemme Expert Selection Perfectly (un)Done, Cure Care, Suave Tropical Coconut or Daily Clarifying
LI (if needed):
Tresemme Perfectly (un)Done, Renpure Brazilian Keratin Straightening (old formula), Cure Care
Stylers: HETT, AIF
PT: IAGirl's as needed