Would a dairy free substitute work such as: almond milk, coconut milk, or soy milk?

I did a cursory google search on some websites that specialize in dairy-free cooking. They all said that coconut milk is comparative to heavy cream. You could try it! Good luck!

Not an expert on dairy-free cooking, but I think you'll really struggle - the setting is dependent on the acid reacting with milk proteins and fat (sort of like making homemade ricotta). I doubt it would even work with a milk instead of cream because of its lower fat content.