If brunost has goat milk in it, it should be labeled geitost (Norwegian for "goat cheese") or gjetost (the old Danish/Norwegian spelling). I've had Ekte Gjetost, a pure goat brunost, and the flavor is significantly sharp. Ski Queen Gjetost is a blend of goat and cow milk. It's much more candy-like, but I expect you still wouldn't like it.
I doubt that anyone is importing cow-only brunost. But if some were available, you might find it a bit more palatable. It's basically dulce le leche with cream added back to it. Now if you don't like dulce le leche, you're out of luck.