Homemade coconut milk in coffee compared to store bought

I've been making my own homemade coconut milk recently because I don't like the list of ingredients (thickeners, emulsifiers, etc.) typically found in store-bought coconut milk.

The problem is, I really like the taste of store-bought coconut milk when I use it in coffee, because I think it tastes remarkably similar to real milk. So, I would actually like to mimic the store-bought version at home. I don't care as much about the consistency as I do about the richness and flavor (or lack of flavor, actually).

At first, I thought I could just water down the coconut milk I usually make and that would be the end of it. However, it's still not quite the same. The homemade version tastes fine by itself, but when I use it to make lattes in the morning there's a certain bitterness/sharpness I can taste. (Note: when I make homemade almond milk, I can also taste that same bitter/sharp flavor as soon as I pair it with espresso). The store-bought version tastes smooth and clean by comparison, just like real milk. I know it's not the espresso at fault, because it tastes good when I make an Americano or a regular dairy milk latte.

So, apart from the thickeners, emulsifier and fortification, store-bought coconut milk must be processed differently. In short, how do they take the coconut taste out of coconut milk while still keeping somewhat of a rich creaminess?