This sounds similar to a dip I make. Instead of tomatoes (and salt and citric acid), I use sun-tried tomato paste, which is saltier and more acidic than tomatoes. I do not use cayenne pepper, but rather dried and ground tepin peppers from the garden. Another difference is that I do not add white pepper.
As for the stabilizer, I assure you it is xanthan gum. I use this is all my hot sauces, salad dressings, and some BBQ sauces. It is natural, an kind of the opposite of corn starch. While it is a thickener, when exposed to sheer forces it becomes more liquid rather than more solid. This makes it perfect for sauces and dressings- shake the bottle, it comes out easy, then thickens and sticks to the food. In the case of this dip, the addition on xanthan gum makes it easier to process in a blender yet still remain a thick dip.
I'll dig out my recipe and mess around with it a bit. I have never tasted the dip, but perhaps I cam help you recreate it.