Is it possible to edit the loot table for a mob that is on fire or killed with Fire Aspect?

I'm making a mod which overhauls the Minecraft food system and makes cooked foods like steak or cooked porkchop a mid game item requiring you to use nether wart to make those cooked foods, and them being easy to get kinda ruins the entire point of the mod. I already overrode the smelting recipes for these cooked meats and know you can technically edit existing loot tables by overriding them with the loot table tool, but I don't see a loot table that specifies a mob that's on fire or killed with a Fire Aspect weapon in the loot tables list since doing so gives you the cooked varient of the animal's raw meat drop. Is there some extra bit of code I can do or an alternative way to do this? I'm fairly new to modding. Thanks!