LCLF says a baking soda cleanse is preferred over a sulfate shampoo to remove silicone buildup, but I've never found anything definitive that says baking soda clarification will remove cones. I think I'd choose the safe /proven route and use a low poo with Cocamidopropyl Betaine, since that ingredient is known to remove silicones.
CG since 11/2011
2c /3a F /Mii, low porosity

Summer Products /Routine:
Clarifying: ACV rinses, Suave Professional Men Deep Clean Peppermint
Low Poo: Renpure Luxurious Argan Oil
Co-washes: VO5 Kiwi Lime Squeeze or Strawberries & Cream
RO:
Tresemme Expert Selection Perfectly (un)Done, Cure Care, VO5 KLS
LI (if needed):
Tresemme Perfectly (un)Done, VO5 KLS, Cure Care
Stylers: FSG, L'Oreal Studio Clean gel, Tresemme Flawless Curls Bouncy Curls, LALSG
PT: IAGirl's as needed