*To Make Dairy-Free:
Use refined coconut oil in place of the oil and dairy-free cream cheese such as Tofuit brand.
**To Make Egg-Free:
To make egg-free, substitute 1 tablespoon fat such as butter or refined coconut oil for each egg yolk and 2 tablespoons of liquid from a can of cannellini beans for each egg white.
I would imagine egg replacer would work well too since it is a dense cake.
https://glutenfreerecipebox.com/gluten-free-gooey-butter-cake/