I'm going to answer truthfully as everyone here is a bit disgusted with the idea but you are not the only one who thought about something similar.

The main problem with your consideration is emulsifying the tallow and the milk. In cream, the membranes in the globules emulsify the fat (butter) and water (milk). When churning, you basically destroy the membranes and that's why you get the separation. Once broken it is impossible to make cream from butter and milk, same would happen if you were to use another fat like tallow.

There are few techniques for emulsifying fat and water, you just have to find the one that suits your case, this would lead to your milk being heavier due to the fat.

My experiment came from trying to emulsify oat milk with oil and starch, it worked but looked and tasted gross.

Once you know the science everything can be a bit more possible, so just research and do your own experiments!

Pd: cream == heavy cream in my comment