We have a certain customer, lets name him Free Customer, all their orders are always 100% discount. Is there any way when they create a Sales Order and the item fulfillment is Shipped, that instead of hitting the COGS account we make it hit another account just for this customer? My initial instincts are telling me no

No native way. May use custom GL plugin to update the GL impact on item fulfilment or create a JE via script.

could utilize allocation schedules to allocate the impact for that customer to another account

I'd go with Custom GL Lines, create JE via script is possible, but the challenge with JE is to capture the event if the cost being recalculated by NS costing engine