Minecraft builtin recipes don't work this way.
One option I can think of is to create an "uncooked jerky" item that only exists to be on the campfire and find a way for your beef strip item to place four of them into the campfire when used, rather than placing itself. You'll have to see how the campfire accepts items and find a way to inject a different item than the one you're holding (and then do it four times, rather than once). That uncooked item is then the one that gets cooked (and the only way to obtain it normally would be to pick it up off the campfire before it's done cooking / break the campfire). Of course this takes up all four cooking slots.
Alternatively you could have an intermediary "cooked beef strip" item that when picked up or dropped turns itself into four beef jerky (there's hooks for both of these actions, I'm pretty sure--OnEntityUpdate is the one for it being dropped on the ground though its Mojang name might be different, not sure about picking it up, but there should be some kind of Item method or Forge event that would work).
Or you treat the act of eating as durability loss rather than item consumption (but this effectively lowers max stack size to 4).