How much foreign substance can I add to processed cheese?
I would experiment with more cheese and less added liquid to make it more firm, making sure the pureed mushrooms are as tiny as possible (Pacotize, homogenize, etc.), and if that still gives an inferior texture try adding some sodium citrate. It sounds like you want to add a minimal amount of liquid and enough emulsification to make sure the water-soluble parts of the mushrooms and flavoring stay put.